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THE  ARGUMENT 
FOR  A  FINITIST  THEOLOGY 


BY 

RAY  HARBAUGH  DOTTERER 


A  DISSERTATION 

!:  JBMITTED  TO  THE   BOARD  OF   UNIVERSITY  StU    J'S  OF   THE 

Johns  Hopkins  University  in  Conformity  with  the 
Requirements  for  the  Degree  of  Doctor 
of  Philosophy 


PRESS  OF 

THE  NEW  ERA  PRINTING  COMPANY 

LANCASTER,  PA. 


EXCHANGE 


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THE  ARGUMENT 
FOR  A  FINITIST  THEOLOGY 


BY 

RAY  HARBAUGH  DOTTERER 


A  DISSERTATION 

Submitted  to  the  Board  of  University  Studies  of  the 

Johns  Hopkins  University  in  Conformity  with  the 

Requirements  for  the  Degree  of  Doctor 

OF  Philosophy 


PRESS  OF 

THE  NEW  ERA  PRINTING  COMPANY 

LANCASTER,  PA. 

I917 


PKEFACE. 

It  was  my  first  intention  to  take  Vaihinger's  PhilosopJiie 
des  ALS  OB  as  the  subject  of  my  doctoral  dissertation;  and 
in  the  spring  of  1916  in  partial  fulfilment  of  the  requirements 
for  the  Master's  degree  I  did  submit  an  essay  on  The  Philos- 
ophy of  the  As  If  in  Its  Application  to  Theology,  I  became 
convinced,  however,  as  the  investigation  proceeded,  that  an  ex- 
amination of  the  doctrine  of  a  ^^  finite  God  "  ought  to  precede 
any  attempt  to  appraise  the  value  of  the  method  of  conscious 
illusion. 

I  gladly  avail  myself  of  the  opportunity  afforded  by  a  preface 
to  acknowledge  my  indebtedness  to  Professor  A.  O.  Lovejoy 
for  his  encouragement  and  for  his  patient  as  well  as  searching 
and  helpful  criticism.  As  I  owe  much  more  to  his  lectures 
and  to  his  oral  and  written  suggestions  than  to  his  published 
writings,  this  general  statement  may  take  the  place  of  par- 
ticular acknowledgments  and  references  in  detail,  which  in  the 
nature  of  the  case  could  not  often  be  given. 

R.  H.  .D. 


TABLE  OF  CONTENTS. 

CbAPter  Pase 

I.  Introductory  Considerations 1-10 

II.  The  Monistic  Absolute  as  the  Philosophic  Equiv- 
alent of  God 11-21 

III.  The  Doctrine  of  a  Finite  God 22-31 

IV.  Theological  Finitism  as  the  Outcome  of  a  Rational 

Theodicy 32-39 

V.  Logical  Finitism  and  the  Idea  of  God 40-49 

VI.  Theology  and  the  "  New  Infinite  " 50-70 

VTI.  Concluding  Reflections  on  Finitist  Theology  . . .  71-79 

Bibliography    80-82 


I. 


Introductory  Considerations. 

1.  The  Method  of  Theological  Inquiry, — Theology  may 
adopt  any  one  of  three  methods  or  it  may  combine  two  or  all 
of  them  with  varying  emphasis  upon  each.  It  may  appeal  to 
the  immediate  experience  of  the  mystic,  or  it  may  simply 
affirm  and  arrange  in  systematic  form  the  doctrines  authorita- 
tively taught  by  the  Church  and  the  Bible,  or  it  may  depend 
upon  the  "reason"  and  "conscience"  of  the  individual  in- 
quirer. 

The  first  method  would  of  course  be  the  best  if  the  ex- 
perience in  question  were  not  so  rare.  Assuming  that  the  ex- 
perience of  the  mystic  constitutes  a  genuine  insight  into  the 
fundamental  nature  of  reality,  he  nevertheless  stands  in  the 
same  relation  to  his  fellowmen  as  a  man  with  normal  vision 
to  a  race  of  men  blind  from  their  birth.  It  would  be  vain  for 
the  seeing  man  to  discourse  of  the  beautiful  colors  to  be  seen 
on  every  side.  Indeed,  it  would  be  impossible  for  him  to  ex- 
press his  experience  in  words,  since  language  is  a  social 
product,  and  the  social  mind  of  the  hypothetical  race  would 
know  nothing  of  color.  Thus  the  mystic's  direct  vision  of  God 
can  not  be  described  in  terms  which  can  be  understood  by 
ordinary  men,  and,  even  from  his  own  point  of  view  or  from 
that  of  a  fellow  mystic,  his  experience  must  ever  remain  in  a 
measure  ineffable.  Moreover,  the  difficulty  of  the  mystical 
method  is  aggravated  by  the  fact  that  the  non-mystic  may  not 
be  willing  to  grant  the  objectivity  of  the  mystic's  experience. 
And  the  rarity  of  his  experience  may  be  made  a  reason  for 
regarding  it  as  illusory.  Indeed,  it  may  be  very  plausibly 
maintained  that  the  alleged  "revelations"  of  the  traditional 
mystic  are  evidences  of  a  pathological  condition  produced  by 

1 


2  The  Argument  for  a  Finitist  Theology. 

his  long-continued  vigils  and  fastings.  This  hypothesis  is 
suggested,  at  least,  by  phenomena  such  as  those  which  Wil- 
liam James  has  described  under  the  name  of  the  "  anaesthetic 
revelation."^  Accordingly,  the  non-mystic  may  be  justified 
in  believing  that  his  lack  of  the  sense  of  immediate  fellowship 
with  absolute  reality  is  not  an  indication  of  spiritual  poverty, 
but  rather  an  evidence  of  sanity. 

The  second  method — ^that  of  external  authority — received 
a  mortal  wound  in  the  time  of  the  Keformation,  when  it  was 
discovered  that  the  two  sources  of  authoritative  teaching,  the 
Church  and  the  Bible,  did  not  always  agree.  To  be  sure,  the 
Protestant  as  well  as  the  Roman  Catholic  still  retained  the 
method  of  authority.  But  the  mere  knowledge  that  the 
schism  had  occurred  operated  to  impair  the  confidence  of  the 
intelligent  layman  in  authority  of  any  kind ;  and  for  the  theo- 
logically trained  man  the  Protestant  appeal  to  the  Bible  as 
the  only  rule  of  faith  and  practice  contained  the  seed  of  its 
own  destruction.  For  the  careful  study  of  the  sacred  writings 
which  was  logically  required  by  the  formal  principle  of  Prot- 
estantism soon  showed  that  these  writings,  instead  of  contain- 
ing one  uniform  and  consistent  revelation,  contain  several  dif- 
ferent and  even  conflicting  systems  of  doctrine,  and  bear  clear 
evidence  of  having  been  produced  in  much  the  same  way  as 
the  other  sacred  books  of  antiquity.  Thus,  although  this  was 
certainly  not  the  intention  of  the  original  Reformers,  the  log- 
ical and  historical  result  of  the  Reformation  has  been  to  refer 
all  questions  of  doctrine  to  the  "private  judgment"  of  the 
individual  Christian. 

The  third  method,  that  of  reliance  upon  reason  and  con- 
science, is,  accordingly,  the  one  that  is  dominant  at  the  present 
time  at  least  among  enlightened  men  and  women.  Having 
throvm  off  the  authority  of  the  Church,  and  being  distrustful 
of  the  genuineness  of  the  mystic's  experience,  they  take  as 

1  The  Will  to  Believe,  pp.  294  ff.     (Note :  For  full  titles,  etc.,  see  the 
appended  bibliography.) 


Introductory  Considerations.  3 

their  only  criterion  of  truth  the  reasonableness  and  ethical  at- 
tractiveness of  the  doctrines  in  question. 

It  is  important  to  note,  however,  that  these  three  theological 
methods — that  of  the  mystic,  that  of  the  authoritarian,  and 
that  of  the  self-reliant  reasoner — are  almost  never  found  pure. 
The  traditional  mystic  has  usually  been,  or  at  least  supposed 
himself  to  be,  a  loyal  son  of  the  Church ;  and  his  revelations 
have  usually  been  in  superficial  agreement  with  its  teachings. 
St.  Thomas  Aquinas  employs  the  method  of  authority;  but  he 
also  reasons,  so  long,  at  least,  as  reasoning  serves  his  purpose. 
The  "  modern  "  man  is  no  more  consistent.  Theologians  who 
in  theory  have  given  up  the  appeal  to  any  external  authority 
nevertheless  slip  back  now  and  then  into  the  argument  from 
Scripture  and  tradition.  And  among  religious  people  who  are 
not  theologians,  one  result  of  the  modem  revolt  against  the 
authority  of  the  Church  and  the  Book  has  been  a  curious  sen- 
timentalism  in  religious  thinking,  a  sort  of  mitigated  mysti- 
cism, which  exalts  "intuition''  and  "immediate  feeling"  as 
over  against  "reason." 

It  must  be  admitted,  I  think,  that  there  is  a  sense  in  which 
the  Scriptures  possess  authority,  and  ought  to  possess  au- 
thority, even  for  the  completely  emancipated  thinker.  Their 
authority  may  be  described  as  suggestive  rather  than  coercive, 
as  accidental  rather  than  constitutive.  Many  biblical  doc- 
trines are  found  to  be  true,  but  their  truth  neither  consists  in 
nor  is  established  by  their  quality  of  being  biblical.  In  other 
words,  the  authority  of  the  Bible  is  not  like  that  of  a  constitu- 
tion or  of  a  legal  code,  but  rather  like  that  of  a  textbook  in 
chemistry  or  some  other  laboratory  science,  the  statements 
contained  in  which  are  to  be  accepted  or  rejected  by  the  stu- 
dent according  as  they  are,  or  are  not,  experimentally  verified. 

There  is  also  a  relative  justification  for  the  claims  of  "  in- 
tuition," "  instinct,"  or  "  immediate  feeling."  This  justifica- 
tion consists  in  the  obvious  fact  that  "  reason  "  in  the  sense  of 
mere  intellection  is  barren.  Before  there  can  be  any  reason- 
ing in  this  narrow  sense  of  the  term,  there  must  be  (a)  sense- 


4  The  Argument  for  a  Finitist  Theology. 

perception,  and  (Z>)  perception  of  "goods"  or  of  relative 
v^alues.  Viewed  in  this  way,  reason  does  not  bring  forth  truth ; 
it  has  the  humbler  office  of  determining  which  of  the  offspring 
of  "  intuition  "  may  be  worthy  of  preservation  and  ought  to  be 
acknowledged  as  true.  In  other  words,  we  may  be  said  to 
reason  when  we  inquire  which  of  our  immediate  perceptions 
of  fact  or  of  value  are  implied  by  or  are  incompatible  with  other 
immediate  perceptions.  Thus  there  is  a  sense  in  which  both 
sense-perception  and  the  perception  of  values  are  more  fun- 
damental than  reasoning.  But  immediate  perception  alone 
is  not  a  sufficient  criterion  of  truth.  For  one  of  our  percep- 
tions of  fact  is  that  immediate  perceptions,  whether  we  limit 
our  view  to  the  experience  of  one  mind  or  consider  the  ex- 
perience of  a  larger  or  smaller  group,  are  not  all  logically  com- 
patible; and  that  they  ought  to  be  logically  compatible  is  one 
of  our  perceptions  of  value.  If  this  perception  of  value  is  to 
be  accepted  as  genuine,  some  immediate  perceptions  and  some 
inferences  from  such  perceptions  must  be  rejected  as  illusory 
or  mistaken.  But  when  immediate  perceptions  are  found  to 
be  mutually  repugnant,  that  is  to  say,  when  it  is  impossible  for 
all  of  them  to  be  genuine  in  the  same  logical  universe,  the 
only  arbiter  that  can  decide  between  them  is  the  reason.  In- 
deed this  deciding  between  incompatible  verdicts  of  "  intui- 
tion ''  is  what  we  mean  by  reason,  when  we  say  that  the  method 
of  theology  must  be  the  method  of  reason,  rather  than  of  mys- 
tical experience  or  of  dependence  upon  authority.^ 

2.  The  Religious  Value  of  the  Idea  of  God. — ^We  value  the 
idea  of  God,  and  seek  to  convince  ourselves  that  the  idea  is 
"  real,''  because  we  feel  the  need  of  God.  Our  interest,  how- 
ever, is  practical  rather  than  theoretical.  As  far  as  the  man 
of  science  is  concerned  there  may  be  a  God ;  but  the  scientist 
long  ago  discovered  that  he,  as  scientist,  has  "  no  need  of  that 
hypothesis."  If,  for  example,  a  geologist  should  tell  us  that 
the  strata  of  rocks  occur  in  a  given  order  because  God  laid 
them  down  in  that  way,  or  if  a  botanist  should  say  that  a  cer- 

2  Cf.  Russell,  Scientific  Method  in  Philosophy,  pp.  21  f . 


Introductory  Considerations.  5 

tain  flower  has  five  petals  because  God  made  it  thus,  even  the 
least  enlightened  theist  would  admit  that  the  assertion  is  from 
the  standpoint  of  science  irrelevant.  And,  in  general,  to  "  ex- 
plain "  the  occurrence  of  any  particular  phenomenon  or  group 
of  phenomena  by  reference  to  divine  agency  is  an  evasion  of 
the  problem  at  issue. 

The  value  of  the  idea  of  God  is,  then,  to  be  sought  in  the 
domain  of  practice  rather  than  of  theory.  It  is  moral  and 
religious  rather  than  scientific.  Traditional  theology  has 
given  the  Divine  Being  the  attributes  of  omnipotence,  om- 
niscience, omnipresence,  and  moral  perfection.  Modern  the- 
ology places  moral  perfection  first,  and  rightly  insists  that  the 
other  attributes  have  religious  value  only  when  moral  per- 
fection is  presupposed.  First  of  all,  God  is  good ;  and  his  in- 
finite wisdom  and  might  are  subservient  to  his  infinite  love.^ 

Beginning,  then,  with  the  thought  of  the  infinite  goodness 
of  God,  one  use  of  the  notion  of  Deity  at  once  suggests  itself. 
God,  as  the  ahaolutely  good  being,  is  man's  moral  goal  or  pat- 
tern. ^'Be  ye  perfect  as  your  Father  in  heaven  is  perfect," 
becomes  the  maxim  of  the  truly  devout  worshipper.  God  is 
the  supremely  perfect  hero,  the  supreme  object  of  imitation. 

N"ext,  combining  the  notion  of  perfect  goodness  with  that  of 
omniscience,  we  derive  the  idea  of  God  as  the  righteous  and 
completely  informed  Judge  of  human  conduct.  The  more 
naive  worshipper  thinks  of  a  day  of  judgment  at  the  end  of 
the  world;  the  more  sophisticated,  of  a  judgment  continually 
going  on.  Whichever  way  the  thought  is  taken,  the  believer 
in  an  all-wise  and  perfectly  good  Being  has  always  before  him 
the  idea  of  an  impartial  and  all-seeing  Spectator  who  "  search- 
eth  the  reins  and  the  hearts."  What  is  concealed  from  one's 
fellowmen  is  fully  knowa  to  him.  Wherein  one  has  been  mis- 
judged by  his  fellows,  he  is  judged  rightly  by  God.  At  the 
tribunal  of  the  Omniscient  One,  absolute  justice  is  dispensed. 

Furthermore  God  is  all-powerful.  He  is  the  Sovereign  of 
the  Universe.    He  has  created,  and  now  upholds  and  governs 

8  Cf .  Clarke,  Tlie  Christian  Doctrine  of  God,  pp.  70  ff. 


6  The  Argument  for  a  Finitist  Theology. 

all.  Because  he  is  omnipotent  his  universal  purpose  will 
eventually  be  completely  fulfilled.  The  life  of  the  believer 
himself  and  that  of  the  group  to  which  he  belongs  can  not 
become  a  failure.  Defeats  are  merely  reverses,  suffering  is 
chastisement.  Faith  in  an  omnipotent  God  is  the  ground  of 
an  assured  confidence  in  the  ultimate  triumph  of  the  right  and 
the  eternal  survival  of  the  good. 

Lastly,  the  attribute  of  omnipresence  makes  possible  the 
thought  of  a  divine  Companion  and  Friend.  Though  foes 
may  scorn  and  friends  forsake,  there  is  a  heavenly  Father  to 
whom  one  may  ^ee  for  sympathy.  Though  the  believer  is 
alone  in  the  world,  he  is  not  alone,  for  God  is  with  him. 

Such,  crudely  and  inadequately  expressed,  is  the  meaning 
of  God  in  the  experience  of  his  worshippers.  In  a  word,  the 
heart  of  the  true  believer  is  filled  with  peace — with  the  "  peace 
of  God  which  passeth  all  understanding." 

But  the  peace  of  God  is  not  a  peace  of  quiescence.  The  truly 
religious  man  is  not  simply  the  contented  man.  His  content- 
ment is  combined  with  a  divine  discontent  with  himself  and 
his  world.  A  "  spark  "  has  disturbed  his  "  clod."  He,  indeed, 
takes  "  no  thought  for  the  morrow,"  but  he  labors  for  the  mor- 
row and  for  many  days  thereafter.  He  seeks  ^'  first  the  king- 
dom of  God  and  his  righteousness,"  and  yet  is  a  man  of  affairs. 
He  believes  that  the  sin  and  the  suffering  and  the  sorrow  of 
life  have  their  place  in  the  divine  economy,  yet  he  is  a  reformer 
and  seeks  to  make  the  world  better  and  happier. 

3.  Some  Antinomies  in  the  Popular  Notion  of  God. — Such 
a  paradoxical  emotional  attitude  can  hardly  be  supposed  to 
be  grounded  in  a  logically  consistent  doctrine  of  God.  Indeed 
the  paradoxical  character  of  the  typical  religious  experience 
would  suggest  a  self-contradictory  ground.  And  no  very 
profound  study  is  required  to  show  that  the  popular  notion 
of  God  is  shot  through  with  contradictions.  Some  of  these 
are  evident  to  the  popular  mind  itself;  others  do  not  appear 
until  the  notion  is  examined  with  more  than  ordinary  care. 


Introductory  Considerations,  7 

A  few  of  the  more  obvious  of  these  difficulties  are  the  fol- 
lowing. 

{a)  Goodness  versus  Power  in  Relation  to  the  Existence  of 
Evil, — According  to  traditional  theology  the  world  is  partly 
evil,  and  is  nevertheless  the  work  of  Infinite  Power  and  Per- 
fect Goodness.  The  antinomy  is  obvious:  How  can  Omnip- 
otent Goodness  be  supposed  to  have  produced  or  to  be  the 
ground  of  an  imperfect  world?  Attempts  at  reconciliation 
merely  repeat  the  difficulty  in  a  new  form.  Thus  we  hear 
men  say  that  if  God  had  not  permitted  some  particular  evil  a 
greater  evil  would  have  occurred;  that  the  pains  and  suf- 
ferings of  life  are  means  of  chastisement  and  moral  purifica- 
tion; that  sin  makes  possible  forms  of  goodness  which  out- 
weigh both  the  sin  itself  and  the  evil  consequences  resulting 
from  it.  But  it  is  obvious  that  this  mode  of  explanation  itself 
presupposes  some  limitation  of  divine  power.  It  assumes  that 
evil  is  a  necessary  condition  of  the  perfection  of  the  world, 
and  that  even  Omnipotence  is  bound  by  this  condition.  The 
existence  of  evil  is  a  proof  of  God's  inability  to  remove  it 
from  his  world,  or,  what  amounts  to  the  same  thing,  of  his 
inability  to  remove  or  prevent  it  without  defeating  his  uni- 
versal purpose.  Again,  if  we  adopt  the  evolutionary  point  of 
view,  and  admit  the  idea  of  a  temporal  process  into  our  rea- 
sonings about  good  and  evil,  we  may  say  that,  while  God's 
world  is  not  yet  perfect,  its  perfection  will  come  at  the  end  of 
the  evolutionary  process,  ^ut  the  idea  of  evolution,  the  very 
notion  of  a  process,  is  irreconcilable  with  omnipotence.  For 
the  idea  of  a  process  implies  hindrance  or  retardation,  and 
therefore  the  finitude  of  the  energizing  agent. 

(fe)  Righteousness  versus  Predestination, — This  is  a  special 
and  aggravated  case  of  the  preceding  difficulty.  If  God  is 
omnipotent,  he  is  the  absolute  Sovereign  of  his  world,  and  all 
events  are  in  accordance  with  his  will;  but  if  all  events,  in- 
cluding human  actions,  bad  as  well  as  good,  are  willed  by 
God,  then  God  is  the  real  author  of  human  sin. 


N 


8  The  Argument  for  a  Finitist  Theology. 

(c)  The  Hearing  of  Prayer  versus  Omniscience. — If  God 
be  thought  of  after  the  analogy  of  an  ancient  oriental  monarch, 
prayer  may  be  regarded  as  necessary  in  order  to  propitiate  the 
Despot  when  he  is  angry,  or  to  overcome  his  carelessness,  or 
his  indifference  to  the  well-being  of  his  subjects.  But,  surely, 
in  the  case  of  a  Sovereign  who  is  perfectly  good,  prayer  is  not 
needed  for  this  purpose.  Again  if  God's  power  be  limited,  it 
may  be  maintained  with  considerable  plausibility  that  prayer 
is  a  means  of  supplementing  the  energy  which  is  insufficient 
for  the  accomplishment  of  some  good  purpose.  But,  according 
to  the  traditional  doctrine,  there  is  no  defect  of  power,  and 
prayer  can  not  be  justified  in  this  way.  Once  more,  if  God's 
Icnowledge  were  limited,  prayer,  in  the  sense  of  petition  for 
some  definite  boon,  might  be  regarded  as  a  means  of  inform- 
ing God  concerning  human  needs.  The  analogy  of  the  eastern 
monarch  here  recurs,  and  doubtless  has  figured  largely  in  the 
common  theory  of  prayer.  But  if  God  is  omniscient,  we  can- 
not tell  him  anything,  and  the  antinomy  remains  unsolved. 

(d)  Personality  versus  Immutability. — According  to  tra- 
ditional religious  thought,  God  is  a  person,  sl  Friend  or  Father 
with  whom  men  may  enjoy  fellowship.  On  the  other  hand, 
he  is  also  said  to  be  "eternal,"  not  merely  in  the  sense  that 
his  existence  is  without  beginning  or  end,  but  in  the  sense 
that  he  is  supertemporal  and  immutable.  But  the  attributes 
of  personality  and  immutability  are  plainly  contradictory. 
For  a  person  is  the  subject  of  experience,  and  experience  im- 
plies time.  At  any  rate,  human  persons  are  in  time;  succes- 
sion is  of  the  very  essence  of  their  life ;  and  therefore  a  divine 
Person  who  is  assumed  in  any  meaningful  sense  to  know  them 
and  to  fellowship  with  them  must  also  be  in  time. 

4.  A  Prospectus  of  the  Ensuing  Discussion. — ^We  have  seen 
that  the  attempt  to  think  of  God  as  omnipotent,  omniscient, 
and  immutable,  and  at  the  same  time  as  a  personal  Being  who 
is  perfectly  good,  and  who  enters  into  communion  with  men 
and  may  be  influenced  by  their  petitions,  is  logically  impos- 
sible.   Accordingly,  the  next  three  sections  will  be  devoted  to 


Introductory  Considerations,  S 

a  critical  exposition  of  two  rival  attempts  to  rationalize  or  to 
find  a  substitute  for  the  traditional  (Christian)  conception  of 
Deity.  These  contrasted  theories  are  the  theory  of  monistic 
idealism,  which  in  its  specifically  theological  aspect  is  a  theory 
of  the  divine  immanence,  and  that  of  pluralism,  with  its  doc- 
trine of  a  "  finite  "  God.  As  my  examination  of  these  rival 
theories  leads  me  to  the  acceptance  of  the  latter,  I  have  called 
the  whole  discussion  "  an  argument  for  a  finitist  theology." 

God  has  been  said  to  be  infinite  in  two  different  senses:  (1) 
He  has  been  said  to  be  the  Whole  of  reality,  or  at  least  to  be 
the  Ground  and  Source  of  all  that  is.  (2)  He  has  been  said 
to  be  infinite  in  the  literal  numerical  sense  of  the  word;  for 
example,  to  know  an  infinite  multiplicity  of  knowledge-ele- 
ments, or  to  be  "  eternal,"  either  in  the  sense  of  living  through 
an  infinite  sequence  of  moments,  or  in  the  sense  of  being  super- 
temporal  and  yet  in  some  manner  containing  infinite  time. 
The  God  of  monistic  idealism,  for  example  the  "Absolute" 
as  described  by  Jpgiah  BjQXce»  is  held  to  be  infinite  in  both  of 
these  senses.  The  Absolute  is  the  all-inclusive  Reality;  and, 
by  virtue  of  Royce's  fundamental  epistemological  presupposi- 
tions, his  one  eternal  or  timeless  Purpose  includes  or  implies 
an  infinite  multiplicity  of  elements.  Over  against  this  monis- 
tic theory  stand  the  theory  of  John  Stuart  Mill  and  William 
James,  on  the  one  hand,  and  that  of  Charles  Renouvier.  on  the 
other.  These  theories,  which  I  shall  call  respectively  ^^gihical 
finitism"  and  "logical  finitism,"  are  mutually  compatible, 
but,  as  we  shall  see,  do  not  necessarily  imply  one  another. 
The  doctrine  of  a  "  finite "  God  as  it  is  expounded  by  Mill 
and  James  consists  essentially  in  the  denial  of  God's  infinitude 
in  the  former  of  our  two  senses.  According  to  this  view,  God 
is  not  omnipotent.  It  is  a  view  which  is  founded  chiefly  upon 
the  difficulties  of  theodicy,  upon  the  impossibility  of  "  justify- 
ing the  ways  of  God  to  man,"  if  God  is  assumed  to  be  infinite 
in  the  sense  of  possessing  all  knowledge  and  all  power.  Ac- 
cording to  Renouvier  and  his  school,  the  finitude  of  the  world 
and  of  God  logically  results  from  the  self-contradiction  which 
lurks  in  the  conception  of  a  "  realized  infinite." 


10  The  Argument  for  a  Finitist  Theology, 

The  discussion  of  the  theories  of  Eoyce  and  Renouvier  will 
lead  us  to  an  examination  of  the  so-called  New  Infinite  of  re- 
cent mathematics,  as  it  has  been  defined  by  Richard  Dede- 
kind  and  Georg  Cantor;  for  by  his  own  account  the  idealism 
of  Royce  is  logically  dependent  upon  the  validity  of  this  con- 
ception, and  the  entire  Renouvierist  philosophy  must  go  by 
the  board  if,  as  is  maintained,  the  formulation  of  this  new 
definition  of  infinity  frees  the  notion  of  a  realized  infinite 
from  the  difficulties  which  Renouvier  found  in  it.  In  view, 
therefore,  of  the  strategic  importance  of  this  subsidiary  issue, 
I  shall  devote  Section  VI  to  an  examination  of  these  con- 
trasted ways  of  thinking  about  the  infinite.  My  conclusion 
will  be  that  the  formulation  of  the  "  new  "  infinite  has  not  re- 
moved the  logical  objections  to  monistic  idealism,  nor  at  all 
impaired  the  cogency  of  the  reasonings  of  Renouvier  and  his 
disciples. 

The  last  section  will  contain  a  brief  summary  of  all  that 
has  gone  before,  together  with  a  further  examination  of  the 
conception  of  a  "  finite  "  God. 


II. 


The  Monistic  Absolute  as  the  Philosophic  Equivalent 

OF  God. 

In  our  attempt  to  find  a  conception  of  God  that  is  both 
rationally  satisfactory  and  religiously  serviceable  we  turn  to 
the  philosophers.  Two  types  of  theory  may  be  distinguished : 
the  monistic  and  the  pluralistic.  According  to  the  monistic 
theories,  God  is  the  whole  of  existence;  pluralistic  theories, 
on  the  other  hand,  make  God  the  part,  but  the  controlling  part 
of  existence. 

1.  Monistic  Idealism  as  a  Fulfilment  of  Traditional  The- 
ology.— In  this  chapter  we  shall  consider  the  monistic  revision 
of  the  traditional  conception  of  God.  The  theory  of  Josiah 
Koyce  may  be  taken  as  a  typical  expression  of  this  class  of 
theories.* 

Koyce's  conception  of  God  is  regarded  by  its  author,  "not 
as  destroying,  but  as  fulfilling,  the  large  collection  of  slowly 
evolving  notions  that  have  appeared  in  the  course  of  history  in 
connection  with  the  name  of  God."^  He  insists  that  "what 
the  faith  of  our  fathers  has  genuinely  meant  by  God  is,  despite 
all  the  blindness  and  all  the  unessential  accidents  of  religious 
tradition,  identical  with  the  inevitable  outcome  of  a  reflective 
philosophy."^  This  conception  "undertakes  to  be  distinctly 
theistic,  and  not  pantheistic.  It  is  not  the  conception  of  an 
Unconscious  Keality,  into  which  finite  beings  are  absorbed; 
nor  of  a  Universal  Substance,  in  whose  law  our  ethical  inde- 
pendence is  lost;  nor  of  an  Ineffable  Mystery,  which  we  can 
only  silently  adore.     On  the  contrary,  every  ethical  predicate 

*For  Royce's  account  of  his  philosophic  ancestry,  see  The  Beligious 
Aspect  of  Philosophy,  pp.  ix  ff. 

5  Royce,  et  al.,  The  Conception  of  God,  p.  48. 

^Ihid.,  p.  50;  see  also  The  Problem  of  Christianity,  Preface. 

11 


12  The  Argument  for  a  Finitist  Theology. 

that  the  highest  religious  faith  of  the  past  has  attributed  to 
God  is  capable  of  exact  interpretation  in  terms  of  our  present 
view."^ 

Professor  Eoyce's  contribution  to  the  theistic  discussion  con- 
sists, then,  in  the  identification  of  God  with  the  Absolute  of 
idealistic  philosophy;  and  in  attempting  so  to  define  the  Ab- 
solute as,  on  the  one  hand,  to  avoid  the  self-contradictions 
which  are  to  be  found  in  the  notion  of  Deity  as  ordinarily  con- 
ceived, and,  on  the  other  hand,  to  enrich  the  notion  of  the  Ab- 
solute so  that  it  shall  be  a  fit  object  for  the  religious  emotions 
or  attitudes  of  awe  and  reverence,  of  faith,  loyalty,  and  love. 
It  is  important  to  remember,  however,  that  many  idealistic 
philosophers  have  not  been  willing  to  regard  the  Absolute  as 
personal,  or  in  any  significant  sense  as  a  Self.  Thus  Mr.  F. 
H.  Bradley  does  not  apply  the  name  God  to  the  Absolute,^ 
and,  if  Dr.  McTaggart  is  right,  Hegel  himself,  who  is  com- 
monly regarded  as  the  father  of  this  general  way  of  thinking, 
ought  not  to  have  done  so.^  His  use  of  "  God  "  and  of  other 
religious  terms,  says  McTaggart,  was  merely  an  accommoda- 
tion to  the  "current  mythology''  of  the  time.  According  to 
Professor  Royce,  however,  the  Absolute  of  monistic  idealism 
is  what  the  Church  has  really  meant  all  along  by  God;  but 
this  meaning  has  been  only  vaguely  apprehended,  and  there- 
fore only  imperfectly  expressed. 

As  defined  by  Royce,  God,  or  the  Absolute,  includes  in  his 
own  consciousness  and  will  the  content  of  all  finite  minds. 
The  individual  self  is  an  identical  part  of  the  Divine  Self.^^ 

"  Let  us  sum  up,  in  a  few  words,"  says  Royce,  "  our  whole 
argument.  There  is,  for  us  as  we  are,  experience.  Our 
thought  undertakes  the  interpretation  of  this  experience. 
Every  intelligent  interpretation  of  an  experience  involves, 
however,  the  appeal  from  this  experienced  fragment  to  some 

7  Ihid.,  p.  49. 

8  Appearance  and  Beality,  pp.  446  ff. 

0  Studies  in  Hegelian  Cojsmology,  pp.  59  ff.,  213. 

10  The  Conception  of  God,  p.  xiii ;  Eihhert  Journal,  I,  44. 


The  Monistic  Absolute,  13 

more  organized  whole  of  experience  in  whose  unity  this  frag- 
ment is  conceived  as  finding  its  organic  place."-^  -^  "  There 
must  be  an  experience  to  which  is  present  the  .  .  .  actual 
limitation  and  narrowness  of  all  finite  experience."^  ^ 

Furthermore,  since  every  reality  exists  "just  in  so  far  as 
there  is  experience  of  its  existence,"-^  ^  since,  in  other  words, 
everything  that  is,  is  the  content  of  mind,  it  follows  that  the 
"  things  "  which  we  ordinarily  think  of  as  non-mental  are  in- 
cluded in  the  content  of  the  Absolute  Self. 

"  The  reality  that  we  seek  to  know,"  says  Koyce,  "  has  al- 
ways to  be  defined  as  that  which  either  is  or  would  be  present 
to  a  sort  of  experience  which  we  ideally  define  as  an  organized 
— that  is,  a  united  and  transparently  reasonable  experience. 
We  have,  in  point  of  fact,  no  conception  of  reality  capable  of 
definition  except  this  one."^*  "To  assert  that  there  is  any 
absolutely  real  fact  indicated  by  our  experience,  is  to  regard 
this  reality  as  presented  to  an  absolutely  organized  experience, 
in  which  every  fragment  finds  its  place."^^ 

Professor  Royce's  conception  of  the  Absolute  is  attained, 
then,  by  combining  the  traditional  attribute  of  omniscience 
with  the  idealistic  presupposition  that  to  be  is  to  be  known  as 
being.  It  may  be  remarked  in  passing  that  if  this  presuppo- 
sition is  denied,  the  whole  edifice  of  monistic  idealism  falls  to 
the  ground.  We  are  not  now  concerned,  however,  with  the 
question  of  the  existence  of  the  Absolute,  but  only  with  its 
definition.  If  the  presupposition  is  granted,  it  is  evident  that, 
as  Royce  maintains,  "In  order  to  have  the  attribute  of  Om- 
niscience, a  being  would  necessarily  be  conceived  as  essen- 
tially world-possessing."^^ 

The  error  and  suffering  and  sin  of  our  finite  lives  are  all 
due  to  the  fragment ariness  of  our  experiences.     When  taken 

11  The  Conception  of  God,  p.  42. 

12  Ihid.,  p.  41.    Cf.  The  Religious  Aspect  of  Philosophy,  p.  441. 

13  The  Conception  of  God,  p.  43. 
^*Il)id.,  p.  30. 

isl&tJ.,  p.  42. 
i6  76t<2.,  p.  13. 


14  The  Argumeni  for  a  Finitist  Theology, 

up  into  the  infinite  completeness  of  the  Universal  Self,  all  the 
imperfections  of  existence  cancel  out,  or  better,  all  are  re- 
quired to  constitute  the  perfection  of  the  Whole.  We,  as  frag- 
ments of  the  Absolute,  may  be  victims  of  misfortune,  unhappy, 
discontented,  sinful.  But  the  Absolute  is  perfectly  good.  Our 
imperfection,  and  our  thought  of  the  world  as  imperfect,  are 
the  consequence  of  the  limitation  of  our  knowledge.  We  know 
in  part;  the  Absolute  knows  the  Whole,  and  pronounces  it 
complete,  and  perfectly  good.^*^ 

"  Misfortune  comes  to  us,  and  we  ask :  What  means  this  hor- 
ror of  my  fragmentary  experience? — why  did  this  happen  to 
me  ?  The  question  involves  the  idea  of  an  experience  that,  if 
present,  would  answer  the  question.  'Now  such  an  experience, 
if  it  were  present  to  us,  would  be  an  experience  of  a  certain 
passing  through  pain  to  peace,  ...  of  a  certain  far  more  ex- 
ceeding weight  of  glory  that  would  give  even  this  fragmentary 
horror  its  place  in  an  experience  of  triumph  and  of  self-pos- 
session. In  brief,  every  time  we  are  weak,  downcast,  horror- 
stricken,  alone  with  our  sin,  the  victims  of  evil  fortune  or  of 
our  own  baseness,  we  stand,  as  we  all  know,  not  only  in  pres- 
ence of  agonizing  fragmentary  experiences,  but  in  presence  of 
besetting  problems,  which  in  fact  constitute  the  very  heart  of 
our  calamity.  .  .  .  Well,  then,  if  the  divorce  of  idea  and  ex- 
perience characterizes  every  form  of  human  consciousness  of 
finitude,  of  weakness,  of  evil,  of  sin,  of  despair,  you  see  that 
Omniscience,  involving,  by  definition,  the  complete  and  final 
fulfilment  of  idea  in  experience,  the  unity  of  thought  and  act, 
the  illumination  of  feeling  by  comprehension,  would  be  an 
attribute  implying,  for  the  being  who  possessed  it,  much  more 
than  a  universally  clear  but  absolutely  passionless  insight.  An 
Omniscient  Being  could  answer  your  bitter  Why?  when  you 
mourn,  with  an  experience  that  would  not  simply  ignore  your 
passion.  For  your  passion,  too,  is  a  fact.  It  is  experienced. 
The  experience  of  the  Omniscient  Being  would  include  it. 

17  The  Eeligious  Aspect  of  Philosophy,  pp.  444  and  449;  Sources  of  Be- 
ligious  Insight,  p.  224. 


The  Monistic  Absolute.  15 

Only  his  insight,  unlike  yours,  would  comprehend  it,  and  so 
would  answer  whatever  is  rational  about  your  present  ques- 
tion. ...  In  order  to  have  the  attribute  of  omniscience,  a 
being  would  necessarily  ...  be  conceived  as  omnipotent,  and 
also  as  in  possession  of  just  such  experience  as  ideally  ought 
to  be;  in  other  words,  as  good  and  perfect."^ ^ 

2.  Some  Difficulties  of  Monistic  Idealism. — As  has  already 
been  remarked.  Professor  Royce's  proof  that  there  is  such  an 
Absolute  Being  as  he  has  defined,  rests  upon  the  presupposition 
that  all  being  is  being  known,  that  all  existence  is  mental. 
Unless  this  assumption  be  granted,  the  argument  goes  to 
pieces.  Moreover,  in  Chapter  V  we  shall  meet  a  consideration, 
which  will  make  it  impossible  for  us  to  conceive  that  the  Ab- 
solute Self  is  real.  This  is  the  self-contradiction  involved  in 
the  notion  of  a  "  realized  infinite.''  For  the  present,  however, 
I  shall  limit  myself  to  pointing  out  certain  other  difficulties, 
which,  it  seems  to  me,  are  inseparable  from  the  conception  of 
the  Absolute  as  it  is  defined  by  Royce. 

(a)  The  first  of  these  may  be  called  the  religious  difficulty. 
We  may  approach  it  by  considering  a  conception  near  akin 
to  that  of  the  monistic  Absolute,  namely,  the  conception  of 
God  as  immanent  in  his  world.  If  God  is  thought  of  as 
transcendent,  and  the  supernatural  and  the  natural  regarded 
as  mutually  exclusive  categories,  then  the  friend  of  religion 
must  view  the  progress  of  science  with  alarm.  A  division  of 
the  world  between  science  and  religion,  between  Nature  and 
God,  might  be  reasonably  satisfactory,  if  one  could  be  sure 
that  the  boundary  would  remain  permanently  fixed.  But,  if 
we  define  the  natural  as  that  which  is  explicable  in  terms  of 
scientific  law,  then,  as  science  extends  its  territory,  and  pro- 
claims its  belief  in  the  possibility  of  a  universal  conquest,  the 
outlook  for  religion  becomes  dark  indeed.  If  the  supernatural 
is  defined  as  that  which  is  not  natural,  the  scientific  view  of 
the  world  leaves  no  place  for  God. 

In  this  perilous  situation  "liberal"  theologians  have  em- 

18  The  Conception  of  God,  pp.  11  ff. 


16  The  Argument  for  a  Finitist  Theology. 

phasized  tlie  immanence  of  God,  and  have  said  that  all  events 
are  supernatural,  since  all  are  produced  by,  or  are  particular 
expressions  of,  the  immanent  God.  The  difficulty  of  this  pro- 
cedure is,  however,  that,  in  thus  preserving  the  right  to  use 
the  word  God,  we  are  in  danger  of  so  impoverishing  the  idea 
of  God  that  it  becomes  of  little  value  as  a  religious  conception. 
In  order  to  meet  this  peril  it  is  then  necessary  to  insist  that 
God  is  transcendent  as  well  as  immanent.  Thus  to  avoid  the 
danger  of  pantheism.  Dr.  William  Newton  Clarke,  for  ex- 
ample, maintains  that  "  Transcendence  is  first.  ...  It  is  the 
transcendence  that  gives  the  immanence  its  meaning.  .  .  . 
The  Christian  thought  of  God  is  not  so  much  that  the  im- 
manent God  is  transcendent,  as  it  is  that  the  transcendent  God 
is  immanent.''^  ^  The  God  who  is  immanent  is  the  Personal 
God. 

The  difficulty,  however,  is  to  see  how  a  completely  immanent 
God  can  be  personal.  Mei:ely  to  say  that  God  is  immanent, 
and  that  therefore  all  events  are  acts  of  God,  and  that  for  this 
reason  the  theist  need  not  be  troubled  by  the  claim  of  science 
to  include  all  events  in  its  realm ;  and  also  to  swy  that  God  is 
transcendent  and  personal  as  well  as  immanent,  does  not  solve 
the  difficulty ;  any  more  than  to  say  that  a  certain  geometrical 
figure  is  round  and  also  has  four  right  angles  will  remove  the 
self-contradiction  from  the  notion  of  a  square  circle.  In  the 
same  way,  for  Royce  merely  to  say  that  the  Absolute  is  Per- 
sonal, and  that  his  theory  is  a  theism  and  not  a  pantheism  does 
not  suffice.  Unless  we  assume  that  completeness,  as  opposed 
to  fragmentariness,  is  per  se  worthy  of  reverence,  an  assump- 
tion which  is  by  no  means  self-evident,  there  seems  to  be  no 
sufficient  reason  for  worshipping  the  Absolute  f^  and  it  seems 
impossible  for  us  to  enter  into  fellowship  with  such  an  entity, 
unless  we  consciously  or  unconsciously  think  of  it  as  if  it 
were  a  Person  distinct  from,  and  standing  over  against  us  and 
all  others. 

19  The  Christicm  Doctrine  of  God,  p.  322. 

20  See  Professor  Mezes  'a  criticism  of  Koyce  ^s  Ultimate  Being,  The  Con- 
ception of  God,  pp.  54  ff. 


The  Monistic  Ahsolute.  17 

{!))  Furthermore,  there  are  certain  'psychological  difficul- 
ties in  the  conception  of  the  Absolute.  These  result  from  the 
circumstance  that  some  of  our  experiences,  which  are  by  def- 
inition experiences  of  the  Absolute  also,  are  conditioned  by 
our  very  finiteness,  and  therefore  can  not  be  experienced  by 
an  Absolute  being.  Such  experiences  are  hope  and  fear,  for 
example.  A  being  who  knows  perfectly  what  the  morrow  will 
bring  forth  can  not  hope  for  anything  on  the  morrow ;  neither 
can  he  fear.  If  I  am  sure  of  obtaining  a  certain  boon,  I  do 
not  hope  to  obtain  it ;  still  less  can  I  be  said  to  fear  lest  I  shall 
not  obtain  it.  Both  of  these  emotions  presuppose  some  degree 
of  uncertainty  with  reference  to  the  future,  and  such  uncer- 
tainty is  incompatible  with  omniscience.  In  the  same  way  it 
is  impossible  that  an  omniscient  being  should  ever  experience 
curiosity  or  the  joy  of  discovery.  The  Absolute,  too,  must  be 
without  the  experience  of  sin  and  repentance.  Yet,  as  Abso- 
lute, he  must  contain  all  these  experiences. 

If  all  we  mean  when  we  say  that  a  being  is  omniscient  is 
that  he  Jcnows  about  all  the  experiences  of  all  other  beings  (in 
addition  to  all  the  other  knowledge  that  he  is  assumed  to  pos- 
sess), then  these  difficulties  do  not  arise.  The  Absolute  may 
well  enough  be  assumed  to  know  all  about  my  states  of  mind ; 
but  he  cannot  without  contradiction  be  assumed  to  include  in 
the  totality  of  his  experience  the  identical  hopes  and  fears  and 
feelings  of  repentance  that  I  feel. 

The  same  remark  must  be  made  of  our  experience  of  tem- 
poral succession.  God,  or  the  Absolute,  is  said  to  know  all  in 
an  Eternal  Now,^^  But  if  that  is  the  nature  of  his  knowledge, 
it  is  impossible  that  He  should  know  things  in  succession.  It 
must  be  admitted,  however,  that  both  kinds  of  knowledge  are 
attributed  to  him.  It  is  common  to  make  a  distinction  be- 
tween a  holy  place  in  which  a  real  experience  of  succession  is 
found,  and  a  Holy  of  Holies  in  which  all  "  bondage  to  succes- 
sion ''  is  overcome.     Thus  the  late  Professor  Bowne,  although 

21  The  Eeligious  Aspect  of  Philosophy,  p.  441 ;  The  Conception  of  God, 
pp.  59  f . ;  The  World  and  the  Individual,  II,  138  ff. 


18  The  Argument  for  a  Finitist  Theology. 

he  criticizes  the  absolute  idealism  of  the  Hegelian  school  on 
the  ground  that  "such  a  system  excludes  all  movement  and 
progress,  and  the  appearance  of  movement  can  only  be  reck- 
oned a  delusion/'  insists  nevertheless  that  "  from  the  theistic 
standpoint  the  infinite  must  be  viewed  as  possessing  an  eternal 
mind  so  far  as  itself  is  concerned.''  On  the  other  hand,  "  the 
infinite  must  be  in  time,  so  far  as  the  world  process  is  con- 
cerned."^^ 

Dr.  William  E'ewton  Clarke  writes  in  a  similar  strain: 
"  Succession  is  essential  to  the  significance  of  events  in  time, 
and  if  God  had  no  knowledge  of  it  he  could  not  understand 
events  or  the  history  that  is  composed  of  them,  or  the  life  of 
his  children.  He  has  both  kinds  of  knowledge.  He  eternally 
knows  all  things  at  once,  and  is  also  aware  of  them  as  they 
become  realized  in  time  and  space;  and  in  the  perfect  mind 
there  is  no  inconsistency  between  these  two  modes."^^ 

But  does  this  last  clause  mean  anything  more  than  that  con- 
tradictions may  be  tolerated  in  the  case  of  affirmations  con- 
cerning the  perfect  mind,  which  would  be  intolerable  if  the 
mind  were  not  perfect?  And  why  this  reluctance  to  subject 
the  perfect  mind  to  the  "  bondage  of  succession  "  ?  We  may 
say,  if  we  will,  that  God  would  be  limited  by  succession;  but 
is  he  not  limited  in  just  the  same  sense  by  the  law  of  contra- 
diction and  the  law  of  love  ?  The  attempt  to  affirm  the  reality 
of  both  kinds  of  knowledge  in  the  Divine  mind  suggests,  once 
more,  the  attempt  to  define  a  plane  figure  that  is  both  square 
and  circular. 

This  view  can  be  logically  defended  in  no  other  way  than 
by  a  denial  of  the  reality  of  the  experience  of  time.  Says  Pro- 
fessor Mezes,  interpreting  the  view  of  Koyce,  "  Speaking  tech- 
nically, time  is  no  reality ;  things  seem  past  and  future,  and  in 
a  sense,  non-existent  to  us,  but  in  fact  they  are  just  as  gen- 
uinely real  as  the  present  is.  Is  Julius  Csesar  dead  and  turned 
to  clay?    1^0  doubt  he  is.    But  in  reality  he  is  also  alive,  he 

22  Metaphysics,  pp.  486,  240  f . 

23  The  Christian  Doctrine  of  God,  p.  346.    Cf .  pp.  295  ff. 


The  Monistic  Absolute,  19 

is  conquering  Spain,  Gaul,  Greece,  Egypt.  He  is  leading  the 
Roman  legions  into  Britain,  and  dominating  the  envious  Sen- 
ate, just  as  truly  as  he  is  dead  and  turned  to  clay — just  as  truly 
as  you  now  hear  the  words  I  am  speaking.  Every  reality  is 
eternally  real ;  pastness  and  futurity  are  merely  illusions."^^ 

But  if  the  experience  of  succession  is  illusory,  what  then  is 
real  ?  The  fact  that  of  two  experiences  one  comes  after  the 
other  is  certainly  as  real  as  anything  can  be.  If  the  two  ex- 
periences are  cognitive,  it  may  indeed  happen  that  the  events 
to  which  they  refer  really  occurred  in  a  different  order  from 
that  in  which  I  have  experienced  them;  or  these  events  may 
really  have  been  simultaneous;  but  the  experiencings  them- 
selves are  in  the  order  in  which  they  come,  and  it  is  meaning- 
less to  say  that  they  are  really  in  a  different  order,  or  that 
they  are  simultaneous.  If  the  Absolute  were  merely  supposed 
to  know  about  them,  he  might  have  knowledge  of  them  both  at 
the  same  moment,  although  I  experience  them  one  after  the 
other ;  but  if  my  experiencings  are  numerically  the  same  as  cer- 
tain experiencings  of  His,  then  the  order  in  which  they  occur 
for  me  must  also  be  the  order  in  which  they  occur  for  Him. 

(c)  Last  and  most  important  of  all  are  the  ethical  diffi- 
culties of  the  conception  of  the  Absolute.  If  all  thoughts  are 
thoughts  of  God,  and  all  events  are  acts  of  God,  then  our  evil 
desires  and  purposes  are  purposes  and  desires  of  God,  and  all 
our  sinful  deeds  are  deeds  of  God.  The  antinomy  between 
predestination  and  the  goodness  of  God,  which  has  troubled 
traditional  and  popular  theology,  thus  appears  in  an  aggra- 
vated form  in  the  theology  of  immanence.  The  logical  conse- 
quence is  a  denial  of  the  genuineness  of  the  distinction  between 
good  and  evil,  right  and  wrong.  If  the  Absolute  must  be  con- 
ceived to  be  "  in  possession  of  just  such  experience  as  ideally 
ought  to  be, "2^  then,  from  the  standpoint  of  the  Absolute,  there 
is  no  reason  for  wishing  that  anything  should  be  other  than  it 

24  Eoyce,  et  al.,  The  Conception  of  God,  p.  60. 
26  The  Conception  of  God,  p.  13. 

26  The  Beligious  Aspect  of  Philosophy,  pp.  454  f . ;  Sowrces  of  Beligious 
Insight,  pp.  237,  224. 


20  The  Argument  for  a  Finitist  Theology. 

is ;  no  reason  for  pronouncing  one  thing  evil  and  another  good. 

The  fact  that  the  partisans  of  the  monistic  Absolute,  like 
believers  in  the  Calvinistic  doctrine  of  predestination,  have 
been  zealous  in  good  works,  and  have  been  strenuous  advo- 
cates of  reform  and  good  haters  of  iniquity  of  all  sorts,  does 
not  alter  the  fact  that  the  logical  consequence  of  their  creed  is 
a  life  of  resignation  and  acquiescence.  If  the  account  which 
monistic  idealism  gives  of  the  world  is  true,  not  only  is  it 
logically  right  for  me  to  endure  my  private  pains  and  disap- 
pointments without  grumbling,  and  to  "  spiritualize "  and 
"idealize"  them,  seeing  that  the  Absolute  is  not  unhappy, 
and  the  Absolute  is  not  disappointed,  and  that  in  spite  of 
these  "partial  evils"  "in  the  universe  as  a  whole  the  good 
triumphs "  f^  but  there  is  no  reason  why  I  should  bestir 
myself  to  lighten  the  sorrows  of  my  fellow  men,  since  their 
sorrows  too,  just  as  they  are,  have  their  proper  place  in  the 
eternal  felicity  of  the  Absolute  and  contribute  to  the  perfec- 
tion of  the  whole. 

It  may  perhaps  be  said  that,  since  nothing  that  we  can  do  can 
disturb  or  impair  the  eternal  perfection  of  the  Absolute,  we 
may  still,  without  lack  of  logical  consistency,  and  without  de- 
fect of  loyalty  to  the  good  of  the  Whole,  attempt  to  brighten 
the  little  comer  in  which  we  are  placed.  But  if  the  present 
proportion  of  light  and  shadow  is  just  the  correct  one  to 
produce  the  perfection  of  the  Whole,  then,  assuming  the 
Whole  to  remain  perfect,  in  brightening  one  corner,  I  should 
automatically  darken  some  other  comer;  and  there  is  no  suf- 
ficient reason  for  wishing  to  do  that.  If,  on  the  other  hand, 
it  should  be  said  that  the  precise  proportion  of  light  and  shade 
in  the  universe  is  a  matter  of  indifference,  and  that  conse- 
quently I  can  seek  my  ovni  happiness  and  that  of  others  with- 
out necessarily  diminishing  the  felicity  of  the  Absolute  or  of 
any  sentient  being,  then  we  should  have  to  conclude  that  the 
doctrine  of  the  Absolute  is  without  any  moral  significance 
whatever;  for,  if  my  pains  and  sorrows  are  not  necessary  to 
the  felicity  of  the  Absolute,  the  doctrine  of  the  Absolute  pro- 
vides no  reason  why  I  should  bear  them  patiently. 


The  Monistic  Absolute.  21 

The  monistic  idealist  is  sure  to  object  at  this  point  that  the 
argument  of  the  last  few  paragraphs  is  based  upon  an  inade- 
quate account  of  Royce's  ethical  theory.  For  Professor  Royce 
speaks  not  only  of  evils  which  are  to  be  endured,  but  also,  and 
much  more,  of  evils  which  are  to  be  overcome;  and,  in  his 
theory,  the  typical  evil  is  not  physical  pain,  or  mere  pain  of 
any  kind,  but  rather  the  bad  will  of  a  moral  agent. 

This  objection  of  the  monistic  idealist,  however,  introduces 
considerations  which  had  better  be  postponed  until  we  have 
given  an  account  of  the  ethical  argument  ifor  theological 
finitism. 


III. 

The  Doctrine  of  a  Finite  God. 

The  monistic  theories  make  a  grudging  admission  of  the 
individual  and  particular  facts  of  life.  The  pluralistic 
theories,  on  the  other  hand,  emphasize  these  facts  and  take 
their  departure  from  them.  For  the  pluralistic  theories  the 
particular  and  the  individual  constitute  the  true  reality.  The 
dirt  and  grime  of  actual  experience  must  not  be  forgotten  or 
ignored  in  the  thought  of  an  Eternal  Reality  which  is  sup- 
posed, in  some  mysterious  or  very  imperfectly  understood 
manner,  to  be  perfect,  though  including  imperfection.  Sin 
and  suffering  are  not  illusions  which  are  overcome  in  an 
Eternal  ^ow,  or  fragmentary  experiences  which  together  form 
the  perfect  Whole  of  existence.  On  the  contrary,  the  victory 
of  the  Good  is  not  yet  achieved;  the  world  is  not  completed; 
the  process  of  evolution  is  a  reality.  God  is  not  all-powerful ; 
but  he  is  a  Struggler,  who  is  hindered  and  thwarted,  at  least 
for  the  time  being,  by  necessities  which  are  beyond  his  con- 
trol. The  time  process  is  required  for  the  accomplishment  of 
his  good  purposes. 

In  other  words,  by  those  who  hold  the  pluralistic  view  of 
the  world,  the  tradition  that  God  is  Absolute,  Infinite,  Om- 
nipotent, Omniscient,  Immutable,  etc.,  is  definitely  and  con- 
sciously abandoned;  and,  if  the  belief  in  God  is  retained,  he 
is  thought  of  as  a  finite  being,  one  among  many,  yet  supreme 
above  all. 

This,  in  broad  outline,  is  the  doctrine  of  God  expounded  by 
John  Stuart  Mill,  William  James,  and  other  philosophical 
radicals. ^^     They  were  not  afraid  of  unorthodox  phraseology, 

27  For  more  recent  expositions  of  the  finitist  doctrine,  see  H.  G.  Wells, 
God  the  Invisible  King,  and  E.  H.  Eeeman,  Do  We  Need  A  New  Idea  of 
God? 

22 


The  Doctrine  of  a  Finite  God,  23 

they  were  not  much  influenced  by  the  mere  form  and  sound 
of  words.  Most  theological  and  religious  writers,  on  the  other 
hand,  and  many  philosophers,  manifest  a  curious  reverence  for 
words  and  phrases  that  have  been  hallowed  by  long  use  and  a 
corresponding  reluctance  to  accept  new  forms  of  expression. 
They  are,  accordingly,  disposed  to  shy  at  such  a  word  as  finite 
when  it  is  employed  as  an  adjective  modifying  the  term  God; 
and  yet  many  of  them  are  not  in  principle  so  far  as  they  seem 
from  the  view  suggested  by  the  phrase  formed  of  these  two 
words.  Thus  many  monistic  idealists  have  held  that  suffering 
must  be  a  genuine  experience  of  the  Absolute;  and  it  has 
become  a  commonplace  of  moral  and  religious  exhortation  to 
say  that  we  are  co-workers  with  the  Omnipotent.  We  may 
question  the  logical  consistency  of  Absolutist  philosophers  and 
religious  exhorters,.  and  yet  rejoice  that,  even  in  opposition  to 
the  logical  implications  of  their  systems,  they  have  sought  to 
be  loyal  to  the  facts  of  human  experience. 

In  the  fifth  chapter  we  shall  consider  the  arguments  of  those 
who  have  arrived  at  a  finitist  theology  by  a  logical  analysis  of 
the  notion  of  the  realized  infinite.  These  thinkers  have  come 
to  the  conclusion  that  it  is  impossible  without  logical  incon- 
sistency to  say  that  anything  that  is,  is  infinite.  Therefore 
neither  God  nor  the  world  can  be  said,  if  we  speak  strictly,  to 
be  infinite.  In  this  and  the  immediately  following  chapter, 
we  shall  restrict  our  attention  to  what  may  be  called  the  ethical 
argument  for  the  doctrine  that  God  is  finite. 

This  argument  is  essentially  a  theodicy,  an  attempt  to  jus- 
tify the  ways  of  God  to  men  in  view  of  the  manifest  evil  and 
imperfection  of  the  world.  In  brief,  the  argument  is  this; 
God  can  not  be  thought  to  be  at  once  omnipotent  and  perfectly 
good.  If  we  say  that  he  is  omnipotent,  that  his  sovereignty  is 
complete,  that  all  events  that  occur  are  willed  by  him ;  then  it 
follows  that  he  is  responsible  for  the  actual  world,  which  is 
partly  evil,  and,  accordingly,  that  he  is  not  perfectly  good. 
If  we  begin  at  the  other  end,  and  say  that  God  is  perfectly 
good,  then  we  must  deny  that  he  is  omnipotent. 


24  The  Argument  for  a  Finitist  Theology. 

John  Stuart  Mill  may  be  taken  as  a  representative  of  this 
general  tendency.  His  argument  rests  upon  the  evident 
cruelty  and  recklessness  of  Nature,  from  which  he  infers  the 
limited  power  of  the  Author  of  JSTature.  ^'  I^ext  to  the  great- 
ness of  these  cosmic  forces,  the  quality  which  most  forcibly 
strikes  everyone  who  docs  not  avert  his  eyes  from  it,  is  their 
perfect  and  absolute  recklessness.  They  go  straight  to  their 
end,  without  regarding  what  or  whom  they  crush  on  the  road. 
...  In  sober  truth,  nearly  all  the  things  which  men  are 
hanged  or  imprisoned  for  doing  to  one  another,  are  nature's 
everyday  performances.  Killing,  the  most  criminal  act  recog- 
nized by  human  laws,  xTature  does  once  to  every  being  that 
lives.  .  .  .  E'ature  impales  men,  breaks  them  as  if  on  the 
wheel,  casts  them  to  be  devoured  by  wild  beasts,  bums  them 
to  death,  crushes  them  with  stones  like  the  first  Christian 
martyr,  starves  them  with  hunger,  freezes  them  with  cold, 
poisons  them  by  the  quick  or  slow  venom  of  her  exhalations, 
and  has  hundreds  of  other  hideous  deaths  in  reserve,  such  as 
the  ingenious  cruelty  of  a  ISTabis  or  a  Domitian  never  sur- 
passed. All  this,  l^ature  does  with  the  most  supercilious  dis- 
regard of  mercy  and  of  justice.  .  .  .  ISText  to  taking  life  is 
taking  the  means  by  which  we  live ;  and  ^Nature  does  this,  too, 
on  the  largest  scale  and  with  the  most  callous  indifference.  A 
single  hurricane  destroys  the  hopes  of  a  season;  a  flight  of 
locusts,  or  an  inundation,  desolates  a  district ;  a  trifling  chem- 
ical change  in  an  edible  root,  starves  a  million  of  people.  .  .  . 
Everything  in  short,  which  the  worst  men  commit  either 
against  life  or  property  is  perpetrated  on  a  larger  scale  by 
natural  agents.  .  .  .  All  which  people  are  accustomed  to 
deprecate  as  '  disorder '  and  its  consequences,  is  precisely  a 
counterpart  of  Nature's  ways.  Anarchy  and  the  Eeign  of 
Terror  are  overmatched  in  injustice,  ruin,  and  death,  by  a  hur- 
ricane and  a  pestilence."^^ 

The  main  thesis  of  the  Essay  on  Nature  is  that  it  is  "  irra- 
tional and  immoral"  to  "make  the   spontaneous  course  of 

28  Three  Essays  on  Beligion,  pp.  28  ff. 


The  Doctrine  of  a  Finite  God.  25 

things  the  model"  of  man^s  voluntary  actions.^^  The  inci- 
dental conclusion  of  the  essay  is  the  position  which  has  been 
stated  by  way  of  anticipation,  namely,  that  it  is  absurd  and 
irrational  to  hold  that  God  is  perfectly  good  and  also  all- 
powerfuL  "  The  only  admissible  moral  theory  of  Creation," 
says  Mill,  "  is  that  the  Principle  of  Good  cannot  at  once  and 
altogether  subdue  the  powers  of  evil,  either  physical  or  moral. 
.  .  .  Those  who  have  been  strengthened  in  goodness  by  rely- 
ing on  the  sympathizing  power  of  a  powerful  and  good  Gov- 
ernor of  the  world,  have,  I  am  satisfied,  never  really  believed 
that  Governor  to  be,  in  the  strict  sense  of  the  term,  omnip- 
otent. They  have  always  saved  his  goodness  at  the  expense 
of  his  power." ^^  Recurring  to  the  same  thought  in  the  essay 
on  the  Utility  of  Religion,  Mill  contends  that  "  one  only  form 
of  belief  in  the  supernatural — one  only  theory  respecting  the 
origin  and  government  of  the  universe — stands  wholly  clear 
both  of  intellectual  contradiction  and  of  moral  obliquity.  It 
is  that  which,  resigning  irrevocably  the  idea  of  an  omnipotent 
creator,  regards  Nature  and  Life  not  as  the  expression  through- 
out of  the  moral  character  and  purpose  of  the  Deity,  but  as 
the  product  of  a  struggle  between  contriving  goodness  and  an 
intractable  material,  as  was  believed  by  Plato,  or  a  principle 
of  evil,  as  was  the  doctrine  of  the  Manichseans."^^ 

Mill  shows  that  all  the  attempts  that  are  made  to  escape 
this  conclusion  are  futile,  and  tacitly  presuppose  it.  "That 
much  applauded  class  of  authors,  the  writers  on  natural  the- 
ology, .  .  .  have  exhausted  the  resources  of  sophistry  to  make 
it  appear  that  all  the  suffering  in  the  world  exists  to  prevent 
greater — that  misery  exists,  for  fear  lest  there  should  be 
misery :  a  thesis  which,  if  ever  so  well  maintained,  could  only 
avail  to  explain  and  justify  the  works  of  limited  beings,  com- 
pelled to  labor  under  conditions  independent  of  their  own  will ; 
but  can  have  no  application  to  a  Creator  assumed  to  be  om- 

2»  lUd.,  p.  64. 
30  lUd.,  pp.  39  f . 
81  lUd.,  p.  116. 


26  The  Argument  for  a  Finitist  Theology. 

inpotent,  who,  if  he  bends  to  a  supposed  necessity,  himself 
makes  the  necessity  which  he  bends  to.  If  the  maker  of  the 
world  can  all  that  he  will,  he  wills  misery,  and  there  is  no 
escape  from  the  conclusion." 

If  we  nevertheless  attempt  to  escape  by  saying  that  "the 
goodness  of  God  does  not  consist  in  willing  the  happiness  of 
his  creatures,  but  their  virtue,"  Mill  replies  that  "if  the 
Creator  of  mankind  willed  that  they  should  all  be  virtuous, 
his  designs  are  as  completely  baffled  as  if  he  had  willed  that 
they  should  all  be  happy."^^ 

"But,  it  is  said,  all  these  things  are  for  wise  and  good 
ends."  It  may  be  said  that  "we  do  not  know  what  wise 
reasons  the  Omniscient  may  have  had  for  leaving  undone 
things  which  he  had  the  power  to  do.  It  is  not  perceived  that 
this  plea  itself  implies  a  limit  to  Omnipotence.  When  a  thing 
is  obviously  good  and  obviously  in  accordance  with  what  all 
the  evidences  of  creation  imply  to  have  been  the  Creator's  de- 
sign, and  we  say  we  do  not  know  what  good  reason  he  may 
have  had  for  not  doing  it,  we  mean  that  we  do  not  know  to 
what  other,  still  better  object — ^to  what  object  still  more  com- 
pletely in  the  line  of  his  purposes,  he  may  have  seen  fit  to  post- 
pone it.  But  the  necessity  of  postponing  one  thing  to  another 
belongs  only  to  limited  power.  Omnipotence  could  have  made 
the  objects  compatible.  Omnipotence  does  not  need  to  weigh 
one  consideration  against  another.  .  .  .  l^o  one  purpose  im- 
poses necessary  limitations  on  another  in  the  case  of  a  Being 
not  restricted  by  conditions  of  possibility."^^ 

Therefore  "  the  notion  of  a  providential  government  by  an 
omnipotent  Being  for  the  good  of  his  creatures  must  be  en- 
tirely dismissed."^^  If  we  believe  that  God  is  all-powerful 
and  that  iN'ature  is  his  handiwork,  our  "worship  must  either 
be  greatly  overclouded  by  doubt,  and  occasionally  quite  dark- 
ened by  it,  or  the  moral  sentiments  must  sink  to  the  low  level 
of  the  ordinances  of  Mature:  the  worshipper  must  learn  to 

32  Ihid.,  p.  37. 

33  iMd.,  pp.  179  f. 

34  ihid.,  p.  243. 


The  Doctrine  of  a  Finite  God.  27 

think  blind  partiality,  atrocious  cruelty,  and  reckless  injustice, 
not  blemishes  in  an  object  of  worship,  since  all  these  abound  to 
excess  in  the  commonest  phenomena  of  Nature.  .  .  .  He  who 
comes  out  with  least  moral  damage  from  this  embarrassment, 
is  probably  the  one  who  .  .  .  confesses  to  himself  that  the 
purposes  of  Providence  are  mysterious,  that  its  ways  are  not 
our  ways,  that  its  justice  and  goodness  are  not  the  justice  and 
goodness  which  we  can  conceive  and  which  it  befits  us  to  prac- 
tise. When,  however,  this  is  the  feeling  of  the  believer,  the 
worship  of  the  Deity  ceases  to  be  the  adoration  of  abstract 
moral  perfection.  It  becomes  the  bowing  down  to  a  gigantic 
image  of  something  not  fit  for  us  to  imitate.  It  is  the  worship 
of  power  only."^^ 

The  very  argument  which  has  been  chiefly  relied  upon  to 
prove  the  existence  of  God,  namely,  the  argument  from  design, 
far  from  establishing  his  omnipotence,  is  easily  shown  to  be 
incompatible  with  it.  "It  is  not  too  much  to  say  that  every 
indication  of  Design  in  the  Kosmos  is  so  much  evidence 
against  the  Omnipotence  of  the  Designer.  For  what  is  meant 
by  Design  ?  Contrivance :  the  adaptation  of  means  to  an  end. 
But  the  necessity  of  contrivance — the  need  of  employing  means 
— ^is  a  consequence  of  the  limitation  of  power.  .  .  .  Wisdom 
and  contrivance  are  shown  in  overcoming  difficulties,  and  there 
is  no  room  for  them  in  a  Being  for  whom  no  difficulties  exist. 
The  evidences,  therefore,  of  Natural  Theology  distinctly  im- 
ply that  the  author  of  the  Kosmos  worked  under  limitations; 
that  he  was  obliged  to  adapt  himself  to  conditions  independent 
of  his  will,  and  to  attain  his  ends  by  such  arrangements  as 
those  conditions  admitted  of."^^ 

A  creed  like  this  makes  human  life  significant.  "A  vir- 
tuous human  being  assumes  in  this  theory  the  exalted  char- 
acter of  a  fellow-laborer  with  the  Highest,  a  fellow-combatant 
in  the  great  strife ;  contributing  his  little,  which  by  the  aggre- 
gation of  many  like  himself  becomes  much,  towards  that  pre- 
ss ihid.,  pp.  112  f. 
86  ihid.,  pp.  176  n. 


28  The  Argument  for  a  Finitist  Theology. 

gressive  ascendancy,  and  ultimately  complete  triumph  of  good 
over  evil,  which  history  points  to,  and  which  this  doctrine 
teaches  us  to  regard  as  planned  by  the  Being  to  whom  we  owe 
all  the  benevolent  contrivance  we  behold  in  l^ature."^^ 

Mill's  position  is  enthusiastically  endorsed  by  William 
James  in  his  volume  on  A  Pluralistic  Universe,  "  When  John 
Mill  said  that  the  notion  of  God's  omnipotence  must  be  given 
up  if  God  is  to  be  kept  as  a  religious  object,  he  was  surely  ac- 
curately right ;  yet  so  prevalent  is  the  lazy  monism  that  idly 
haunts  the  region  of  God's  name,  that  so  simple  and  truthful 
a  saying  was  generally  treated  as  a  paradox.  God,  it  was  said, 
could  not  be  finite.  I  believe  that  the  only  God  worthy  of  the 
name  must  be  finite."^^  With  all  its  ambiguities  and  incon- 
sistencies, the  common  conception  of  God  is  at  bottom  that  of 
a  finite  Being.  The  God  of  David  or  of  Isaiah,  the  Heavenly 
Father  of  the  'New  Testament,  is  not  the  Absolute.  "  That 
God,"  says  James,  "  is  an  essentially  finite  being  in  the  cosmos, 
not  with  the  cosmos  in  him."  "  The  God  of  our  popular 
Christianity  is  but  one  member  of  a  pluralistic  system.  He 
and  we  stand  outside  of  each  other,  just  as  the  devil,  the  saints, 
and  the  angels  stand  outside  of  both  of  us."^^ 

Mill's  polemic  is  directed  against  the  doctrine  of  omnip- 
otence as  held  by  traditional  orthodoxy;  that  of  James  is  di- 
rected against  the  conception  of  the  Absolute,  which  has  been 
supposed  by  its  adherents  to  solve  diflSculties  such  as  those 
raised  by  Mill.^^  "  The  absolute,"  insists  James,  "  taken 
seriously,  and  not  as  a  mere  name  for  our  right  occasionally  to 
drop  the  strenuous  mood  and  take  a  moral  holiday,  introduces 
all  those  tremendous  irrationalities  into  the  universe  which  a 
frankly  pluralistic  theism  escapes,  but  which  have  been  flung 
as  a  reproach  at  every  form  of  monistic  theism  or  pantheism. 
It  introduces  a  speculative  ^problem  of  evil'  namely,   and 

37  IJ)id.,  p.  117. 

38  James,  A  Pluralistic  Universe,  p.  124. 

39  Ibid.,  pp.  110  f . ;  see  also  The  Will  to  Believe,  pp.  116  and  134  f . 

40  Beligious  Aspect  of  Philosophy,  p.  453 ;  Sources  of  Beligious  Insight, 
pp.  240  ff. 


The  Doctnne  of  a  Finite  God.  29 

leaves  us  wondering  why  the  perfection  of  the  absolute  should 
require  just  such  hideous  forms  of  life  as  darken  the  day  for 
our  human  imaginations.  If  they  were  forced  upon  it  by 
something  alien,  and  to  'overcome'  them  the  absolute  had 
still  to  keep  hold  of  them,  we  could  understand  its  feeling  of 
triumph,  though  we,  so  far  as  we  were  ourselves  among  the 
elements  overcome,  could  acquiesce  but  sullenly  in  the  resultant 
situation,  and  would  never  just  have  chosen  it  as  the  most 
rational  one  conceivable.  But  the  absolute  is  represented  as 
a  being  without  environment,  upon  which  nothing  alien  can 
be  forced.  ...  Its  perfection  is  represented  as  the  source  of 
things,  and  yet  the  first  effect  of  that  perfection  is  the  tre- 
mendous imperfection  of  all  finite  experience."^  ^ 

To  this  the  partisan  of  the  Absolute  will,  of  course,  object 
that  the  imperfection  of  the  finite  is  a  logically  indispensable 
condition  of  the  perfection  of  the  Infinite.  And  not  only  the 
monistic  idealist,  but  the  defender  of  traditional  theology  may 
take  this  position.  Thus  St.  Augustine  long  ago  taught  that 
evil  does  not  disturb  the  order  and  beauty  of  the  universe ;  for 
"  as  a  painting  with  dark  colors  rightly  distributed  is  beau- 
tiful, so  also  is  the  sum  of  things  beautiful  for  him  who  has 
power  to  view  them  all  at  one  glance,  notwithstanding  the 
presence  of  sin,  although,  when  considered  separately,  their 
beauty  is  marred  by  the  deformity  of  sin.  God  would  not  have 
created  those  angels  and  men  of  whom  he  knew  beforehand 
that  they  would  be  wicked,  if  he  had  not  also  known  how  they 
would  subserve  the  ends  of  goodness."  "  The  whole  world 
thus  consists,  like  a  beautiful  song,  of  oppositions. "^^  Or,  to 
employ  an  illustration  of  the  Platonic-Augustinian  doctrine 
which  is  repeated  by  Royce,  "  as  one  looking  over  the  surface 
of  a  statue  with  a  microscope,  and  finding  nothing  but  a  stony 
surface,  might  say,  how  ugly!  but  on  seeing  the  whole  at  a 
glance  would  know  its  beauty ;  even  so  one  seeing  the  world  by 
bits  fancies  it  evil,  but  would  know  it  to  be  good  if  he  saw  it 

41 A  Plv/ralistic  Universe,  p.  117. 

*2  Ueberweg,  Geschichte  der  PMlosophie,  161  f . 


30  The  Argument  for  a  Finitist  Theology. 

as  a  whole.  And  the  seeming  but  unreal  evil  of  the  parts  may 
be  necessary  in  order  that  the  real  whole  should  be  good."*^ 

This,  however,  is  not  precisely  the  view  of  Royce  himself. 
He  is  not  content  to  say  that  the  evil  must  exist  to  sd;  the 
good  off  by  way  of  contrast.  He  maintains  that  the  "  evil  will 
is  a  conquered  element  in  the  good  will,  and  as  such  is  neces- 
sary to  goodness."  "Goodness  .  .  .  has  as  its  elements  the 
evil  impulse  and  its  correction.  The  evil  will  as  such  may  be 
conquered  in  our  personal  experience,  and  then  we  are  our- 
selves good ;  or  it  may  be  conquered,  not  in  our  thought  con- 
sidered as  a  separate  thought,  but  in  the  total  thought  to  which 
ours  is  so  related,  as  our  single  evil  and  good  thoughts  are 
reilated  to  the  whole  of  us.  .  .  .  As  the  evil  impulse  is  to  the 
good  man,  so  is  the  evil  will  of  the  wicked  man  to  the  life  of 
God,  in  which  he  is  an  element."^* 

The  doctrine  which  we  have  found  in  the  earliest  of  Pro- 
fessor Royce's  books  is  found  also  in  those  which  appeared 
shortly  before  the  end  of  his  life.  Thus  in  The  Sources  of 
Religious  Insight  he  writes  of  evils  "  which  cannot,  yes,  which 
in  principle,  and  even  by  omnipotence,  could  not,  be  simply 
removed  from  existence  without  abolishing  the  conditions 
which  are  logically  necessary  to  the  very  highest  that  we  know. 
Life  in  the  spirit  simply  presupposes  the  conditions  that  these 
ills  exemplify.  .  .  .  Such  sorrows,  such  idealized  evils,  which 
are  so  interwoven  with  good  that  if  the  precious  grief  were 
wholly  removed  from  existence,  the  courage,  the  fidelity,  the 
spiritual  self-possession,  the  peace  through,  in,  and  beyond 
tribulation  which  such  trials  alone  make  possible,  would  also 
be  removed,  surely  show  us  that  the  abstract  principle :  *  Evil 
ought  to  be  abolished,'  is  false."^^ 

Royce  holds  that  a  world  like  the  one  we  know,  which  con- 
tains courage,  fidelity,  etc.,  and  the  evils  which  make  these 
noble  human  qualities  possible,  is  ethically  preferable  to  a 

43  Religious  Aspect  of  Philosophy,  p.  265. 

44  Ihid.,  pp.  455  f . 

45  Sources  of  B,eligious  Insight,  pp.  250  ff.  See  also  The  Problem  of 
Christianity,  I,  308  and  elsewhere. 


The  Doctrine  of  a  Finite  God.  31 

world  which  would  contain  no  evil  and  therefore  none  of  the 
virtues  which  presuppose  it.  For  him  the  ideally  perfect 
whole  is  not  composed  of  none  but  perfect  parts.  On  the  con- 
trary the  imperfection  of  some  of  the  parts  is  a  logical  con- 
dition of  the  complete  perfection  of  the  whole.  To  such  rea- 
sonings, James  replies  that  "the  ideally  perfect  whole  is  cer- 
tainly that  whole  of  which  the  parts  also  are  perfect — if  we 
can  depend  on  logic  for  anything,  we  can  depend  on  it  for  that 
definition.''  Is  then  a  whole  that  consists  of  parts  all  of 
which  are  themselves  perfect  ethically  preferable  to  a  whole 
the  perfection  of  which  includes  some  imperfection,  and,  in- 
deed, consists  at  least  in  part  in  the  overcoming  of  imperfec- 
tion ?  Here  we  have  the  issue  between  the  pluralistic  and  the 
monistic  ethics  in  a  nutshell.  In  the  next  chapter  we  shall 
consider  this  issue  in  so  far  as  it  is  relevant  to  the  problem  of 
theodicy. 


IV. 


Theological  Finitism  as  the  Outcome  of  a  Eational 

Theodicy. 

If  the  world  is  conceived  in  a  pluralistic  or  dualistic 
fashion,  the  case  for  theological  finitism  is  complete.  MilFs 
argument  is  unanswerable.  If  we  think  of  God  as  a  Person 
who  stands  in  moral  relations  with  other  persons,  then,  even 
if  we  assume  these  others  to  be  his  creatures,  it  is  impossible 
to  hold  that  he  is  omnipotent  and  at  the  same  time  perfectly 
good.  The  notion  of  omnipotence  is,  in  itself,  logically  unob- 
jectionable: it  is  logically  possible  to  hold  that  the  Supreme 
Being  is  omnipotent.  But,  if  he  is  omnipotent,  he  is  either 
malevolent  or  else  non-moral.  The  Supreme  Being  might  be 
one  who  would  take  pleasure  in  the  sufferings  of  his  creatures, 
only  doling  out  to  them  sufficient  satisfactions  to  induce  them 
to  continue  the  business  of  living ;  or  he  might  be  wholly  indif- 
ferent to  their  joys  and  sorrows.  Such  a  being,  however, 
would  not  deserve  to  be  called  God ;  for  God,  we  say,  is  good. 
But  if  God  is  good,  then  he  is  not  omnipotent. 

1.  The  Failure  of  Monistic  Theodicy. — In  this  section  I 
propose  to  show  that,  if  we  think  of  the  world  monistically ,  a 
rational  theodicy  is  impossible.  Let  us  then,  for  the  present, 
ignore  the  logical  and  psychological  difficulties  of  monistic 
idealism,  except  as  we  shall  find  them  to  be  bound  up  with  its 
ethical  difficulties.  Let  us  assume  the  monistic  theory  of  the 
world  and  inquire  concerning  its  treatment  of  the  problem  of 
evil. 

It  is  one  of  the  merits  of  Koyce's  discussion  that  he  insists 
upon  finding  a  solution  that  shall  be  rational.  He  does  not 
demand  the  right  to  make  mutually  contradictory  statements 
about  God,  on  the  ground  that  it  is  about  God  that  he  is 

32 


Theological  Finitism  the  Outcome  of  Rational  Theodicy.  33 

speaking.  He  is  not  satisfied  with  saying  that  in  some  way 
that  is  wholly  mysterious  to  us  partial  evil  may  be  universal 
good.  The  Platonic-Augustinian  analogy  of  the  beautiful  pic- 
ture which  is  composed  of  dark  as  well  as  light  colors^^  is  not 
satisfactory  to  him.  It  gives  us  no  enlightenment  as  to  why 
just  these  particular  evils  are  necessary  to  make  the  perfec- 
tion of  the  whole.  It  suggests  an  ethics  of  quietism;  for  it 
logically  implies  that  the  distinction  between  good  and  evil  is 
mere  appearance  and  not  genuinely  valid. 

For  Royce,  then,  evil  is  not  merely  "  an  illusion  of  the  par- 
tial view;  .  .  .  but  .  .  .  seems  in  positive  crying  opposition 
to  all  goodness."  "  We  do  not  say  that  evil  must  exist  to  set 
the  good  off  by  way  of  contrast.  .  .  .  We  say  only  that  the 
evil  will  is  a  conquered  element  in  the  good  will,  and  is  as 
such  necessary  to  goodness."  "  The  good  act  has  its  existence 
and  life  in  the  transcending  of  experienced  present  evil." 
"  Goodness  as  a  moral  experience  is  for  us  the  overcoming  of 
experienced  evil;  and  in  the  eternal  life  of  God  the  realiza- 
tion of  goodness  must  have  the  same  sort  of  organic  relation  to 
evil  as  it  has  in  us."^*^  According  to  the  theory  of  monistic 
idealism,  then,  evil  has  its  place  in  the  perfect  world.  It  is 
the  condition  of  the  possibility  of  the  good.  Even  the  worst 
conceivable  evil,  the  deed  of  a  traitor,  may  be  the  condition  of 
an  atoning  deed  by  which  the  world  is  so  re-created  and  trans- 
formed that  it  is  "  better  than  it  would  have  been  had  all  else 
remained  the  same,  but  had  that  deed  of  treason  not  been  done 
at  all."^8 

'Now  no  one  will  question  the  reality  and  importance  of  the 
experiences  and  social  situations  employed  to  illustrate  the 
"  overcoming "  of  evil.  Physical  pain  sweetens  and  sanc- 
tifies the  life  of  those  who  accept  it  resignedly,  and  bear  it 
patiently.  One  who  meets  his  troubles  bravely  may  thus  make 
them  stepping-stones  to  a  level  of  character  which  he  could  not 
otherwise  have  attained.     As  we  study  the  record  of  human 

46  666  Chapter  III. 

*7  The  Beligious  Aspects  of  Philosophy,  pp.  456  ff. 

*8  The  ProUem  of  Christianity,  I,  308. 


34  The  Argument  for  a  Finitist  Theology. 

progress,  we  frequently  meet  cases  in  which  an  act  of  sin  seems 
to  have  been  the  indispensable  condition  of  great  good.  The 
conception  of  the  "  overcoming  '^  of  evil  is  then  undoubtedly  a 
conception  of  great  significance.  JSTevertheless,  the  theodicy 
offered  by  monistic  idealism  is  not  satisfactory.  The  monistic 
theodicy  fails  for  two  reasons :  (a.)  It  does  not  account  for  all 
evils;  and  (h)  its  account  of  evil  tacitly  presupposes  a 
pluralistic  view  of  the  world. 

(a)  If  the  only  evil  were  an  evil  will,  and  the  only  good  a 
good  will,  then  the  notion  of  the  "  overcoming  '^  of  evil  would 
be  much  less  unsatisfactory.  Let  us  grant  for  the  sake  of  the 
argument,  that  the  will  may  be  good  or  evil  in  itself,  that  is  to 
say,  without  reference  to  the  consequences  likely  to  flow  from 
its  choices  (a  theory  which  is,  however,  very  hard  to  under- 
stand). But,  even  if  we  grant  that  will  may  be  good  or  bad 
'per  se,  there  is  no  reason  to  hold  that  there  are  no  other  goods 
and  evils.  The  enumeration  of  "  goods  "  is  a  sort  of  personal 
confession  of  faith.  I^o  ultimate  rational  ground  can  be  given 
for  calling  anything  good  or  bad.  The  perception  of  values  is 
a  presupposition  of  all  reasoning  about  right  or  wrong,  good 
or  bad.  Certainly,  no  one  will  claim  that  the  goodness  or 
badness  of  will  can  be  logically  demonstrated.  And  all  that  I 
am  insisting  upon  here  is,  that,  if  we  recognize  good  or  bad 
will,  we  are  also  justified  in  speaking  of  other  "goods"  and 
"evils." 

One  of  these  other  goods  is  pleasure,  and  one  of  these  other 
evils  is  pain.  ITow  it  is  true  that  in  many  cases  pain  sub- 
serves a  good  purpose,  and  that  the  patient  endurance  of  pain 
(and,  still  more,  I  should  say,  the  effort  to  relieve  and  destroy 
it  in  oneself  and  in  others)  evokes  some  of  the  most  admirable 
human  qualities ;  but  no  one  has  proved  that  all  pains  are  pro- 
ductive of  sufficient  good  to  justify  their  existence,  and,  as  we 
shall  see  below,  this  attempted  justification  of  pain  presup- 
poses a  non-monistic  view  of  the  world. 

Another  "  good  "  is  life,  considered  apart  from  its  pains  and 
pleasures.    The  corresponding  "  evil "  is  death,  especially  pre- 


Theological  Finitism  the  Outcome  of  Rational  Theodicy,  36 

mature  death.  An  earthquake  destroys  a  thousand  men;  a 
child,  previously  strong  and  healthy,  falls  a  prey  to  a  con- 
tagious disease,  in  consequence  of  the  ignorance  or  careless- 
ness of  its  parents  and  the  negligence  of  the  community.  If 
the  life  of  the  person  has  ceased,  he  cannot  be  said  to  havb 
been  strengthened  or  ennobled  by  the  misfortune  that  has 
befallen  him.  If,  on  the  other  hand,  we  assume  that  the  per- 
son is  immortal,  and  that  his  moral  development  continues  in 
spite  of  what  we  call  death,  there  is  no  reason  for  holding  that 
his  character  has  been  improved  by  his  unfortunate  experience, 
or  that  it  was  in  any  sense  good  for  him  that  his  entrance  into 
the  next  world  should  have  been  hastened  through  human 
ignorance  and  sin.  In  either  case,  there  is  no  reason  for  be- 
lieving that  the  perfection  of  the  Absolute  requires  the  termi- 
nation of  human  lives  in  this  manner. 

Another  "good''  is  sound  intelligence,  and  the  correspond- 
ing "  evil,"  insanity.  This  presents  an  especially  difficult  case 
for  the  monistic  idealist.  The  physical  life  continues,  but  all 
opportunity  for  moral  achievement  is  cut  off.  The  evil  is 
surely  not  overcome  in  the  individual,  and  there  is  no  reason 
for  supposing  it  to  be  overcome  in  the  Absolute,  unless,  indeed, 
one  is  willing  to  hold  that  mere  variety  of  content  is  to  be 
so  highly  esteemed,  that  the  content  of  the  perfect  Mind  must 
be  assumed  to  include  the  insane  delusions  of  these  unfor- 
tunates. Very  similar  considerations  confront  us  when  we 
think  of  those  cases  in  which  men's  wills  have  been  weakened 
by  disease ;  or  in  which  immature  moral  agents  are  compelled 
by  economic  conditions  to  live  in  an  environment  that  is  con- 
ducive to  sin. 

ISTow  so  long  as  there  remains  a  single  evil  that  cannot  ra- 
tionally be  supposed  to  be  "overcome,"  or  even  that  cannot 
be  rationally  shown  to  be  overcome,  we  must  conclude  that  the 
monistic  theodicy  has  failed.  It  is,  of  course,  possible  to  find 
a  great  many  oases  in  the  life  of  the  race,  as  also  in  the  ex- 
perience of  the  individual  moral  agent,  where  evil  seems  to 
have  been  thus  overcome.     But  these  cases  may  be  matched 


36  The  Argument  for  a  Finitist  Theology. 

with  others  where  just  the  contrary  seems  to  be  true.  The 
"  treason  "  of  the  sons  of  Jacob  led  eventually  to  the  elevation 
of  their  brother  to  the  virtual  kingship  of  Egypt,  and  to  the 
preservation  of  the  whole  Israelite  clan  from  famine ;  but  the 
assassination  of  Abraham  Lincoln  led  to  bitter  days  in  the 
life  of  the  American  people,  which,  there  is  reason  to  believe, 
might  have  been  shortened  or  prevented,  if  the  great  President 
had  been  permitted  to  live  a  few  years  longer.  To  be  sure,  we 
do  not  know  what  the  course  of  events  would  have  been,  had 
Lincoln  served  out  his  second  presidential  term;  but  neither 
do  we  know  what  the  course  of  events  would  have  been,  if 
the  brethren  of  Joseph  had  never  sinned,  or  if  Judas  had  not 
betrayed  his  Lord. 

As  we  look  back  over  our  lives,  we  see  temptations  over- 
come and  difficulties  bravely  met  and  conquered;  but  what 
shall  we  say  of  the  temptations  that  were  not  overcome,  of  the 
difficulties  that  were  not  conquered  ? 

Professor  Royce  himself  speaks  of  a  class  of  evils  that,  so 
far  as  we  can  see,  are  not  overcome.  "  Pestilence,  famine,  the 
cruelties  of  oppressors,  the  wrecks  of  innocent  human  lives  by 
cruel  fortunes — all  these  seem,  for  our  ordinary  estimates, 
facts  that  we  can  in  nowise  assimilate,  justify,  or  reasonably 
comprehend.  ...  To  such  evils,  from  our  human  point  of 
view,  the  principle :  ^  They  ought  to  be  simply  driven  out  of 
existence,'  is  naturally  applicable  without  limitation."^^ 

These  evils,  then,  are  not  seen  to  be  necessary  to  the  per- 
fection of  the  universal  good.  They  are  not  yet  "  spiritual- 
ized." But,  then,  with  respect  to  all  such  evils,  the  theodicy 
is  not  rational.  Unfortunately,  philosophy  must  be  written 
"  from  our  human  point  of  view."  So  far  as  these  evils  are 
concerned,  we  are  no  farther  on  than  were  Plotinus  or  Augus- 
tine. All  we  can  say  is  that,  in  spite  of  certain  ugly  black 
spots,  the  picture  may  be  beautiful  as  a  whole  for  a  Mind  that 
can  behold  it  thus. 

(h)  Our  second  reason  for  rejecting  the  monistic  theodicy 

*9  Sources  of  Religious  Insight,  p.  233. 


Theological  Finitism  the  Outcome  of  Rational  Theodicy,  37 

is  that  it  tacitly  presupposes  a  pluralistic  view  of  the  world. 
What  can  we  make  of  the  claim  that  evil  is  "  f ragmentari- 
ness"?  Is  fragmentariness,  as  such,  evil?  Then  nothing  is 
really  good  except  the  Whole ;  and  the  contrast  of  "  good  "  and 
"bad"  is  identified  with  the  contrast  between  the  "more  in- 
clusive "  and  the  "  less  inclusive."  But  why  the  more  inclusive 
should  be  regarded  as  better,  and  the  all-inclusive  as  best  of 
all,  is  by  no  means  clear. 

Well,  then,  does  "overcoming"  mean  more  than  the  mere 
relation  of  Whole  to  part?  If  it  is  to  have  any  ethical  sig- 
nificance, it  certainly  must  mean  more  than  this.  Some  parts 
of  the  Absolute,  to  wit  good  men  and  good  impulses,  are 
"  good  " ;  others  are  "  evil " ;  and  this  difference  is  not  a  dif- 
ference of  size,  or  of  complexity  of  organization.  There  is 
here  a  genuine  difference  of  character;  and  therefore  if  the 
notion  of  "  overcoming "  is  to  have  any  moral  significance  at 
all,  the  evil  that  is  overcome  must  be  not  merely  a  'part  of  the 
Absolute,  but  a  something  other  than  the  Absolute.  For  this 
reason  James  is  right  in  saying  that  the  ideally  perfect  whole 
is  that  whole  of  which  the  parts  also  are  perfect.'^^  It  may 
not  be  true  that  the  ideally  perfect  world,  or  the  ideally  per- 
fect group  of  moral  agents,  is  that  world  or  group  all  the  parts 
of  which  are  perfect;  but  this  is  true  of  a  whole;  for  within  a 
whole  it  is  logically  impossible  for  good  and  evil  to  come  into 
conflict.  Moral  "overcoming"  implies  a  conflict  of  persons, 
or  at  least  of  numerically  distinct  forces,  tendencies,  or  im- 
pulses; and  not  merely  a  contrast  of  parts  with  one  another 
or  with  their  Whole. 

Furthermore,  if  monistic  idealism  is  not  to  give  us  an  ethics 
of  acquiescence,  if  the  notion  of  "  overcoming  "  is  to  be  taken 
seriously,  we  must  assume  the  reality  of  temporal  succession. 
All  the  illustrations  of  the  overcoming  of  evil,  the  case  of  the 
traitor  and  all  cases  in  which  a  person  is  strengthened  and  en- 
nobled by  misfortune,  imply  the  notion  of  time.  If  it  were 
possible  to  assign  any  meaning  at  all  to  the  notion  of  a  time- 
■50  The  Plv/ralistio  Universe,  p.  123. 


38  The  Argument  for  a  Finitist  Theology, 

less  act,  it  might  be  possible  to  think  of  an  eternal  'prevention 
of  evil ;  but  not  of  an  eternal  overcoming  of  evil. 

2.  The  Outline  of  a  Finitist  Theodicy. — In  so  far,  then, 
as  the  conception  of  "overcoming"  is  valid  and  morally  sig- 
nificant, it  presupposes  a  finitist  theology.  If  we  no  longer 
try  to  think  of  God  as  all-inclusive,  and  no  longer  think  of 
him  as  omnipotent,  then  this  conception  of  the  logical  neces- 
sity and  practical  value  of  evil  is  a  conception  of  great  im- 
portance. But  we  need  not  affirm  that  all  evils  are  necessary 
for  the  perfection  of  the  world.  We  may  admit  the  reality  of 
stem  and  opaque  necessities,  which  can  not  be  transcended, 
which  are  not  completely  understood,  it  may  be,  by  the  Su- 
preme Person  himself. 

The  theological  finitist  may  say  without  logical  inconsistency 
that  it  is  better  that  there  should  be  sin  than  that  no  oppor- 
tunity should  be  afforded  for  freedom  and  personality. 

He  may  say  that  it  is  better  that  the  operations  of  N^ature 
should  be  uniform,  than  that  E"ature,  like  an  over-kind  nurse, 
should  be  continually  stepping  in  to  shield  us  from  the  results 
of  ignorance,  recklessness,  or  indolence. 

He  may  say  that  some  of  the  evils  which  we  endure  are  the 
condition  of  the  prevention  of  greater  evils.  He  may,  there- 
fore, without  inconsistency,  explain  much  of  our  physical  pain 
as  a  warning  against  courses  of  action  that  would  lead  to 
greater  misery. 

He  may  expatiate  upon  the  educative  function  of  suffering 
of  every  description,  and  show  how  its  patient  endurance, 
when  it  is  irremediable,  will  produce  a  beautiful  and  saintly 
character. 

In  short,  the  theological  finitist  may  take  over  into  his  sys- 
tem of  thought  all  the  particular  instances  of  "  compensation," 
but  need  not  attempt  to  show  that  the  "compensation"  is 
complete  or  universal.  Many  evils  exist  which  ought  to  be 
"simply  destroyed";  but  God  is  not  strong  or  wise  enough, 
and  certainly  we  are  not,  to  destroy  them  immediately.  In 
other  words,  the  finitist  may  take  seriously  the  thought  of 


Theological  Finitism  the  Outcome  of  Rational  Theodicy,  39 

evolution  or  progress — a  conception  which  the  absolutist  is 
logically  forbidden  to  entertain. 

"We  have  found  a  thought,"  says  Royce  in  his  first  philo- 
sophical book,  "that  makes  this  concept  of  progress  not  only 
inapplicable  to  the  world  of  the  infinite  life,  but  wholly  super- 
fluous." "  Progress  in  this  world  as  a  whole  is  therefore  sim- 
ply not  needed."^  ^  For  the  theological  finitist,  on  the  con- 
trary, the  concept  of  progress,  far  from  being  "  superfluous," 
is  of  immense  significance.  He  hopes  for,  and  believes  in  the 
possibility  of,  a  better  world ;  and,  while  lamenting  the  logical 
inconsistency  of  his  monistic  brother,  works  by  the  side  of  the 
latter  in  the  effort  to  hasten  the  coming  of  this  better  world. 

«i  The  Beligious  Aspect  of  Philosophy,  pp.  464,  466. 


V. 

Logical  Finitism  and  the  Idea  of  God. 

In  the  preceding  chapters  we  have  come  to  the  conclusion 
that  it  is  impossible  to  think  of  God  as  infinite  in  the  first  of 
the  two  senses  of  the  word.  (See  Chapter  I,  Section  4.)  The 
hard  facts  of  human  experience  forbid  us  to  say  that  God  is 
the  Whole  of  reality,  or  that  he  is  omnipotent.  In  the  present 
chapter  I  wish  to  discuss  the  arguments  of  a  school  of  thinkers 
who  have  maintained  the  logical  absurdity  of  holding  that 
God  is  infinite  in  the  second  of  our  two  senses.  According  to 
these  thinkers  we  cannot  say  without  self-contradiction  that 
God  (or  the  world,  or  anything)  consists  of  or  includes  an 
infinite  multiplicity  of  elements,  or  perdures  through  an  in- 
finite sequence  of  moments.  While  this  theory  and  the  view 
which  I  have  called  "  ethical  finitism "  do  not  imply  each 
other,  inasmuch  as  they  deny  the  infinity  of  God  in  two  dif- 
ferent senses,  yet  these  two  kinds  of  finitism  are  mutually  com- 
patible, and  support  one  another,  since  both  are  opposed  to 
monistic  idealism,  which  maintains  that  God,  or  the  Absolute, 
is  infinite  in  both  senses. 

The  founder  of  this  school  of  thinkers  was  Charles  Kenou- 
vier  (1815-1903),  who  is  said  by  James  to  have  been  the 
"  strongest  philosopher  of  France  in  the  second  half  of  the 
nineteenth  century."^ ^  As  important  disciples  we  may  name 
F.  Pillon,  F.  Evellin,  and  E.  Boutreux.  Henri  Bergson, 
France's  most  eminent  living  philosopher,  has  been  greatly  in- 
fluenced by  Renouvier,  but  it  would  scarcely  be  just  to  call 
him  a  disciple.^  ^ 

"  ISTeocriticism,"  as  the  Renouvierist  philosophy  is  called  in 

52  Problems  of  Philosophy,  p.  163.    This,  the  last  book  of  William  James, 
is  dedicated  * '  to  the  great  Eenouvier  's  memory. ' ' 

53  Thilly,  History  of  Philosophy,  pp.  511  f. 

40 


Logical  Finitism  and  the  Idea  of  God,  41 

recognition  of  its  historic  relation  to  the  system  of  Kant,  is 
characterized  by  Windelband  as  a  synthesis  of  Kant  and 
Comte.  Renouvier,  however,  while  no  doubt  influenced  by 
Comte,  always  emphasized  the  difference  between  his  own 
philosophy  and  positivism.  Positivism  begins  with  a  discus- 
sion of  the  natural  sciences  and  of  the  implications  of  scientific 
method,  and  is  led  to  a  rejection  of  the  notions  of  being-in- 
itself  and  transitive  cause.  ^N^eocriticism  reaches  a  similar 
conclusion  by  a  different  road.  It  "begins  with  the  logical 
investigation  of  mental  phenomena,  .  .  .  and  completes  the 
Humian  critique  of  the  concepts  of  substance  and  causality 
by  means  of  an  apriorism  related  to  that  of  Kant:  in  mental 
phenomena  we  have  to  seek  ^  essentially '  the  laws  of  all  being. 
Thus  neocriticism  is  indeed  phenomenalism,  but  not  empiri- 
cism."5* 

1.  The  Finitist  View  of  the  World. — The  best  introduction 
to  the  philosophy  of  Renouvier  is  a  study  of  the  Kantian  "  an- 
tinomies.'' According  to  the  first  of  these  it  can  be  proved 
that  the  world  has  a  beginning  in  time  and  limits  in  space; 
and  it  can  be  proved  with  equal  cogency  that  it  has  no  begin- 
ning and  no  limits.  The  second  antinomy  affirms  that  every 
compound  substance  consists  of  simple,  that  is  indivisible, 
parts;  and  also  that  there  is  nothing  simple,  but  that  every- 
thing is  infinitely  divisible.  The  third  and  fourth  antinomies 
treat  in  the  same  way  the  issue  of  causality  versus  freedom, 
and  the  question  of  the  existence  of  an  absolutely  necessary 
Being.^^ 

There  are  certain  obvious  weaknesses  or  oversights  in  the 
demonstration.  Yet  it  is  possible  so  to  revise  Kant's  argu- 
ments as  to  make  them  much  more  cogent.^^  If,  then,  the 
demonstration  of  both  thesis  and  antithesis,  in  the  case  of  each 
or  only  of  some  of  these  examples  of  the  conflict  of  reason  with 

«*  Windelband,  Lehrhuch  der  Geschichte  der  Philosophie,  S.  515;  Feigel, 
Der  Franzosische  NeoTcritidsmus,  S.  9. 

55  Kant,  Kritik  der  Beinen  Vernunft,  A,  426-461  (Mueller,  pp.  344  flf.). 

56  See  Renouvier,  Critique  de  la  Doctrine  de  Kant,  pp.  29  f.    Cf.  Les  Di- 
lemmes  de  la  M4taphysique  Pwre. 


42  The  Argument  for  a  Finitist  Theology. 

itself,  be  regarded  as  valid,  the  natural  outcome  might  seem 
to  be  a  thoroughgoing  scepticism,  an  utter  despair  of  the  pos- 
sibility of  attaining  the  right  to  be  certain  about  anything. 
For  if  the  human  reason  thus  falls  into  necessary  self-contra- 
diction, what  ground  have  we  for  trusting  it  even  in  those  cases 
in  which  no  contradiction  is  discoverable?  Such  a  complete 
scepticism,  however,  is  practically  impossible;  and,  accord- 
ingly, it  is  more  common  for  those  who  hold  that  both  the 
theses  and  the  antitheses  are  valid  to  argue  that  the  existence 
of  these  antinomies  constitutes  a  reason  for  the  subordination 
of  the  human  reason  to  the  authority  of  the  Church  or  the 
Bible.  From  these  necessary  conflicts  they  conclude  that 
human  reason  has  its  limits,  that  we  are  not  always  safe  in 
refusing  to  believe  some  propositions,  even  though  they  appear 
to  us  to  be  logically  absurd  or  self-contradictory.  Difficulties 
and  even  self-contradictions  may  be  found  in  the  historic 
creeds,  if  we  look  for  them ;  but  the  same  is  true  of  some  of 
the  most  commonly  received  conceptions,  such  as  the  notions 
of  space  and  time.  Therefore,  these  thinkers  argue,  we  are 
justified  in  believing  "mysteries,''  that  is  to  say,  in  holding 
to  the  truth  of  propositions  that  are  logically  inconceivable.^^ 
In  one  of  his  earliest  philosophical  works,  Le  Manuel  de 
Philosophie  moderne  (1842),  Charles  Renouvier  himself  had 
thought  it  possible  to  believe  both  the  theses  and  the  an- 
titheses of  these  antinomies.^ ^  But  the  Essais  de  Critique 
generale  began  a  polemic  against  this  position  ;^^  and,  in  his 
mature  philosophy,  logical  conceivability,  that  is  to  say,  free- 
dom from  self-contradiction,  became  the  criterion,  not  only  of 
all  valid  thinking,  but  also  of  real  existence.  Thus  it  is  a  car- 
dinal principle  of  the  neo-criticist  school  that  one  of  the  two 
sides  of  each  of  the  mathematical  antinomies  must  be  false. 
There  is  no  meaning  in  saying  that  hoth  are  true.  As  Evellin 
puts  it,  "  To  say  yes  and  no  of  the  same  thing  at  the  same  time 

67  See  Mansel,  The  Limits  of  Eeligious  Thought;  Newman,  The  Gram- 
mar of  Assent;  Hamilton,  Lectures  on  Metaphysics. 

58  Arnal,  Philosophie  Meligieuse  de  Charles  Eenouvier,  p.  29. 

59  Ibid.,  p.  33. 


Logical  Finitism  and  the  Idea  of  God,  43 

and  under  the  same  point  of  view,  this  is  contradiction;  and 
for  the  understanding  contradiction  is  death."^^ 

Accordingly  the  neo-criticists  recognize  the  principle  of 
contradiction  as  the  fundamental  principle  of  thought.  More- 
over, they  refuse  to  exempt  any  topic  of  discussion  whatever 
from  the  sway  of  this  principle.  You  can't  appeal  to  it  in 
order  to  demolish  the  theories  of  other  people,  and  then  refuse 
to  admit  its  universal  validity  when  it  threatens  to  demolish 
some  pet  theory  of  your  own.  This  principle,  they  insist,  is 
essential,  not  only  to  human  intelligence,  but  to  intelligence 
as  such.  You  may  speak  if  you  will  of  an  intelligence  that  is 
higher  than  human ;  but,  unless  the  principle  of  contradiction 
is  a  principle  of  this  higher  intelligence  also,  the  phrase 
"higher  intelligence"  is  a  phrase  without  meaning.  Or,  if 
you  say  that  you  believe  in  "truths  above  reason,"  which  on 
the  plane  of  human  reason  take  the  form  of  self -contradictory 
propositions,  they  will  tell  you  that  you  are  the  dupe  of  words. 
Each  of  the  words  of  a  self-contradictory  proposition  may  in- 
deed have  a  perfectly  clear  and  definite  meaning  when  taken 
separately,  but  the  combination  has  no  meaning,  and  the  so- 
called  proposition  is,  strictly  speaking,  no  proposition  at  all, 
but  merely  a  succession  of  words.  You  may  believe  that  you 
believe  it ;  but  in  reality  you  do  not  believe  it,  for  it  is  neither 
true  nor  false  but  meaningless. 

The  principle  of  contradiction  is  thus  the  comer-stone  of 
the  Renouvierist  philosophy.  ISText  in  importance,  and,  as 
Renouvier  and  his  disciples  maintain,  a  necessary  consequence 
of  it,  is  the  "  principle  of  number."  This  is  the  principle  that 
an  infinite  number  is  a  self-contradictory  notion,  and  that 
there  can  therefore  be  no  actual  infinite.  Again  and  again  in 
his  voluminous  writings^  ^  Renouvier  recurs  to  this  point,  and 
seeks  to  establish  it  in  various  ways,  but  especially  by  an  ex- 
amination of  the  properties  of  the  series  of  cardinal  numbers. 

60  Evellin,  Infini  et  Quantite,  p.  19.  Of.  Eenouvier,  Les  Dilemmes  de  la 
Metaphysigue  Pure,  pp.  2  f . 

61  See  Les  Dilemmes  de  la  MStaphysique  Pure,  pp.  122-125;  Nouvelle 
Monadologie,  p.  35 ;  Logique  G4n4rale,  I,  pp.  46  f .,  57,  and  elsewhere. 


44  The  Argument  for  a  Finitist  Theology. 

A  typical  illustration  of  the  absurdity  of  supposing  that  an 
infinite  unmber  may  actually  be  given  is  borrowed  from  the 
writings  of  Galileo.     It  runs  as  follows: 

"  Suppose  the  series  of  natural  numbers  to  be  given.  We 
can  then  form  another  sequence  composed  exclusively  of  the 
squares  of  the  first,  for  it  is  always  possible  to  find  the  square 
of  a  number.  Thus,  by  hypothesis,  the  second  sequence  will 
have  a  number  of  terms  equal  to  the  number  of  terms  of  the 
first.  'Now  the  first  contains  all  the  numbers,  squares  as  well 
as  not-squares,  while  the  second  contains  only  the  squares. 
The  first  has,  therefore,  a  number  of  terms  greater  than  that 
of  the  second,  since,  containing  all  the  numbers,  it  contains  all 
the  squares,  and  it  contains  besides  the  numbers  that  are  not 
squares.  But  by  hypothesis  or  construction,  these  numbers  of 
terms  are  equal.  Therefore  there  are  some  equal  numbers  of 
which  one  is  greater  than  another.  But  this  consequence  is 
absurd.  Therefore  it  is  absurd  to  suppose  the  natural  series 
of  numbers  to  be  actually  given."^^  ^ow  if  the  natural  series 
of  numbers  were  given,  it  would  of  course  be  an  actually  in- 
finite multitude.  But  we  have  seen  that  it  is  absurd  to  sup- 
pose that  the  entire  series  of  cardinal  numbers  is  given ;  and, 
if  this  is  true  of  the  series  of  numbers,  it  is  obviously  true  of 
every  infinite  series,  since  the  terms  of  any  series  may  be  num- 
bered "one,"  "two,"  "three,"  etc.  Therefore  the  notion  of 
an  actual  infinite  is  absurd.  In  other  words,  every  multitude 
has  a  number ;  but  the  notion  of  an  infinite  number  is  logically 
impossible;  and  therefore  it  is  impossible  that  there  should 
be  any  actually  existing  infinite  multitude. 

Here,  however,  an  important  distinction  is  to  be  made.    We 

should  discriminate  between  the  notion  of  an  infinite  which  is 

merely  potential  and  that  of  an  infinite  in  the  absolute  sense 

of  the  term.     "  The  first  consists  in  this :  that,  however  great 

or  small  we  assume  a  given  entity  to  be,  and  however  much  we 

imagine  it  to  be  increased  by  repeated  multiplications,  there 

62Renouvier,  Les  Principes  de  la  Nature,  p.  37;   also  Ann^  Philoso- 
phique,  1890,  pp.  83  ff. 


Logical  Finitism  and  the  Idea  of  God,  45 

must  still  be  thought  to  be  something  greater  or  smaller.  The 
second  infinite  consists  in  this:  that  a  thing  has  actually  and 
absolutely  so  much  magnitude  or  smallness  that  one  can  not 
imagine  more  of  it."^^  The  first  infinite  is  called  by  Kenou- 
vier  and  his  disciples  the  indefinite.  'Now  the  indefinite  is  a 
clear  idea;  but  of  the  absolute  infinite  it  is  psychologically 
and  logically  impossible  to  form  any  conception.  It  is  evi- 
dent from  the  above  definition  of  the  indefinite  that  it  never 
is,  but  always  becomes.  Accordingly  the  indefinite  may  also 
be  called  the  potential  infinite. 

2.  The  God-Conception  of  the  Logical  Finitist. — Some  of 
the  theological  implications  of  logical  finitism  are  discussed 
by  Pillon  in  the  Annee  Philosophique  for  1890,  in  an  article 
entitled  "La  Premiere  Preuve  Cartesienne  De  L'Existence 
De  Dieu  et  La  Critique  De  L'Infini."  In  this  article,  from 
which  several  citations  have  already  been  made,  Pillon  re- 
minds us  that  Descartes,  after  removing  the  doubt  of  his  own 
existence  by  the  help  of  the  cogito  ergo  sum,  seeks  to  escape 
from  egoistic  idealism  by  means  of  the  idea  of  infinity  or  per- 
fection. The  truth  of  our  ideas  about  an  external  world  is 
inferred  from  the  existence  of  God;  and  the  existence  of  God 
is  inferred  from  our  possession  of  the  idea  of  God. 

"Among  my  ideas  there  is  one  which  represents  a  God, 
sovereign,  eternal,  infinite,  immutable,  omniscient,  and  uni- 
versal creator  of  the  things  which  are  outside  of  him."  This 
idea,  says  Descartes,  must  have  a  cause ;  and  Descartes  assumes 
that  there  must  be  at  least  as  much  "  reality  "  in  the  efficient 
cause  as  in  its  effect.  No  idea  c^  contain  more  objective 
reality  than  the  formal  reality  of  its  cause.  !N'ow,  the  only 
cause  adequate  to  the  production  of  this  idea  of  God,  which  we 
find  in  our  minds,  is  God.  Therefore  God  exists.  Therefore 
the  external  world  is  a  real  world.  Such  is  Descartes's 
reasoning. 

Pillon  remarks  that,  in  assuming  the  general  proposition 
that  the  effect  can  not  be  superior  to  the  efficient  cause,  Des- 

63  L  'AntiSe  Philosophique,  1890,  p.  56. 


46  The  Argument  for  a  Finitist  Theology, 

cartes  reveals  a  failure  to  make  his  original  doubt  as  uni- 
versal as  lie  supposed  he  had  made  it.^'*  If,  with  the  school 
of  Kenouvier,  we  hold  that  there  may  be  first  beginnings,  that 
is  to  say,  uncaused  events,  it  is  evident  that  there  is  no  neces- 
sity for  believing  that  the  effect  can  contain  no  more  ^'  reality  " 
than  the  cause.  For,  in  so  far  as  the  scholastic  principle  is 
regarded  as  demonstrable,  it  rests  upon  the  assumption  that 
every  event  must  have  a  cause.  The  scholastic  philosophers 
reasoned,  and  after  them  Descartes,  that  if  the  effect  con- 
tained more  reality  than  the  cause,  then,  assuming  that  both 
effect  and  cause  are  divisible  into  parts,  some  parts  of  the 
effect  would  be  uncaused,  since  the  more  real  being  would 
have  the  greater  number  of  parts.  If,  however,  we  assume 
that  there  is  no  necessary  connection  between  the  notion  of  a 
beginning  and  that  of  an  effect,  the  scholastic  principle  as- 
sumed by  Descrates  sinks  to  the  level  of  a  pseudo-axiom. 
Accordingly,  even  if  we  do  possess  the  idea  of  an  infinite  and 
perfect  being,  we  are  not  justified  in  arguing  from  the  fact  of 
its  possession  to  the  existence  of  such  a  being. 

Moreover,  says  Pillon,  Descartes  confused  the  notions  of 
infinity  and  perfection.  Descartes  assumes  the  synonymity 
of  the  words  "  infinite ''  and  "  perfect."  But,  "  the  idea  of  the 
perfect,  which  Descartes  and  after  him  Malebranche,  Fenelon, 
Leibniz,  all  the  spiritualist  philosophers  of  the  eighteenth 
century,  as  all  those  of  our  time,  have  always  confounded 
with  that  of  infinity,  should  be  rigorously  distinguished  from 
it.  This  distinction  is  one  of  the  fundamental  theses  of  the 
phenomenalist  criticism." 

"Perfection  is  a  general  idea,  formed  from  the  ideas  of 
diverse  qualities  of  an  excellence  such  as  we  contemplate  with 
unmixed  satisfaction,  and  to  which  we  judge  nothing  that  we 
<;an  imagine  of  the  same  order  to  be  preferable.  These  qual- 
ities are  intellectual  or  moral  or  even  physical:  Such  are 
knowledge,  wisdom,  justice,  goodness,  happiness,  beauty,  etc. 
A  perfect  being  is  a  being  in  which  these  qualities  are  united," 

64  L  'AntiSe  PhUosophique,  1890,  p.  161. 


Logical  Finitism  and  the  Idea  of  God.  47 

and  so  fittingly  and  harmoniously  combined  that  there  is  no 
occasion  for  "  reproach  or  desire."  "  The  ideas  relative  to 
perfection  and  those  which  concern  mathematical  magnitude 
form,,  in  reality,  two  separate  and  irreducible  categories." 
These  categories  rest  upon  two  kinds  of  comparison;  Com- 
parison of  quantity  and  comparison  of  estimation  or  pref- 
erence.^^ The  notion  of  perfection  is  then  one  which  we  can 
make  for  ourselves.  Consequently,  we  do  not  need  to  assume 
the  existence  of  a  perfect  being  in  order  to  explain  the  pres- 
ence of  the  idea  in  our  minds. 

The  notion  of  infinity,  i.  e.,  of  infinity  in  the  absolute  sense, 
we  can  not  make.  But,  says  the  neo-criticist,  we  do  not  really 
possess  this  notion,  because  it  is  logically  contradictory.  The 
causal  relation  of  our  notions  of  infinity  is  just  the  opposite 
of  that  supposed  by  Descartes.  "It  is  not  the  idea  of  the  real 
and  absolute  infinite  impressed  in  our  soul  by  this  infinite, 
which  explains  the  formation  of  our  ideas  of  potential  infinites. 
It  is  our  ideas  of  potential  infinites  drawn  from  ourselves, 
which  have  conducted  us  by  a  process  logically  illegitimate, 
but  psychologically  natural,  to  the  idea  of  the  real  and  absolute 
infinite.  It  is  the  infinites,  apparently  actual,  of  the  spatial 
and  temporal  world  that  have  led  us  to  the  divine  attributes. "^^ 

We  can  not,  therefore,  have  any  valid  conception  of  infinity 
in  the  absolute  sense.     The  world  is  finite  and  God  is  finite. 

3.  The  Attributes  of  the  Finite  God. — The  idea  of  God 
which  was  supposed  by  Descartes  to  have  been  impressed  by 
the  Creator  upon  every  human  mind  represented  God  as  "  sov- 
ereign, eternal,  infinite,  immutable,  omniscient,  omnipotent." 
The  neo-criticist  "  principle  of  number,"  as  we  have  seen,  com- 
pels a  revision  of  this  idea. 

By  Pillon,  as  by  Koyce,^^  omnipotence  is  treated  as  the 
typical  attribute  of  Deity.  We  may  justify  this  method  of 
procedure  on  the  ground  that,  in  the  first  place,  omnipotence 

65  76icZ.,  pp.  51,  lllff. 

66  Ihid.,  p.  110. 

67  See  Chapter  II. 


48  The  Argument  for  a  Finitist  Theology. 

implies  omniscience;  knowing  is  only  a  particular  kind  of 
doing.  ITot  to  know  and  not  to  be  able  to  find  ont  would  be 
not  to  be  able  to  do.  In  the  second  place,  and  conversely,  om- 
niscience implies  omnipotence.  That  knowledge  is  power  is 
attested  by  the  etymological  affinity  of  the  German  Jconnen 
and  hennen,  and  the  English  can  and  cunning,  and  by  the  uses 
of  the  French  verb  savoir.  To  know  how  is  the  same  thing  as 
to  be  able.  An  omniscient  being,  accordingly,  will  know  how 
to  do  all  things,  that  is  to  say,  will  be  able  to  do  all  things,  will 
be  omnipotent ;  and,  on  the  other  hand,  if  logic  forbids  us  to 
think  of  God  as  omniscient,  then  we  can  not  logically  think 
of  him  as  omnipotent  either. 

Pillon  approaches  the  discussion  of  the  divine  omniscience 
from  the  side  of  perfect  foreknowledge.  The  problem  is  to 
reconcile  the  idea  of  perfect  foreknowledge  with  the  neo- 
criticist  principle  of  number,  and  this  reconciliation  is,  of 
course,  impossible. 

Objection  has  frequently  been  made  to  the  idea  of  a  fore- 
knowledge of  "free"  acts.  But  the  objection  which  Pillon  is 
urging  holds  against  the  foreknowledge  of  determined  events 
as  well.  For  "  these  necessary  or  determined  future  events  do 
not  form  a  whole,  a  determined  number,  since  they  are  sup- 
posed to  produce  themselves  in  a  time  which  has  no  limits.  It 
is  an  endless  series,  not  simply  of  possibles,  but  of  necessaries. 
It  is  necessary  to  say  that  the  potential  infinity  of  these  future 
events  finds  itself  in  some  manner  realized  in  the  divine  under- 
standing; or  else  it  is  necessary  to  reject  the  perfect  and  abso- 
lute foreknowledge  even  when  it  is  a  question  of  necessary 
future  events."^ ^ 

Yet  we  may  distinguish  two  sorts  of  omniscience,  or  in  the 
special  case  just  now  in  question,  of  perfect  foreknowledge, 
corresponding  to  the  distinction  previously  made  between  the 
absolute,  or  actual  infinite  and  the  potential  infinite.  There 
is,  accordingly,  a  sense  in  which  it  is  logically  unobjectionable 
to  speak  of  perfect  foreknowledge.     "Does  it  follow  then," 

68  lUd.,  p.  174. 


Logical  Finitism  and  the  Idea  of  God.  49 

concludes  Pillon,  "  that  one  ought  to  regard  as  impossihle  the 
perfection  of  foreknowledge?  Yes,  assuredly,  if  one  makes 
this  perfection  consist  in  the  knowledge  of  an  infinite  number 
of  future  realities.  No,  if  in  place  of  attributing  to  the  being 
who  is  supposed  to  be  perfect  a  "single  infinite  and  eternal 
thought,"  one  admits  that  his  intelligence  differs  from  ours  by 
its  extent,  and  not  in  respect  of  its  nature;  that  it  proceeds 
like  ours  by  separate  and  successive  acts  of  thought ;  that  it  is 
free  to  push  back  successively  the  limits  of  its  horizon,  but  that 
it  is  always  obliged  to  have  a  horizon.  Thus  understood  om- 
niscience presents  no  contradiction. '^^^  In  other  words  God 
might,  so  far  as  the  purely  logical  argument  is  concerned,  be 
assumed  to  be  omniscient,  in  the  sense  of  knowing  all  that  is 
at  any  given  moment  knowable,  even  if  he  is  finite  in  the  sense 
of  the  neo-criticist. 

Accordingly,  the  view  of  Mill  and  James  and  of  the  previous 
chapter  is  not  logically  bound  up  with  that  of  Kenouvier  and 
Pillon.  Logical  finitism  suggests  and  makes  room  for,  but 
does  not  in  itself  require  ethical  finitism.  As  has  already  been 
said,  our  reasons  for  denying  the  divine  omnipotence  and  om- 
niscience are  not  merely  logical ;  they  are  chiefly  ethical.  Yet 
the  neo-criticist  argument  prepares  men's  minds  for  the  ac- 
ceptance of  this  ethically  grounded  argument.  Both  argu- 
ments presuppose  loyalty  to  the  principle  of  contradiction, 
and  both  presuppose  a  certain  freedom  from  the  traditional 
preference  for  such  words  as  "infinite,"  "omniscient,"  "om- 
nipotent," etc.,  when  employed  as  adjectives  modifying  the 
word  "God." 
«» Ilid.y  p.  179. 


VI. 
Theology  and  the  "ITew  Infinite." 

When  Renouvier  wrote  his  principal  works  he  could  say 
that  the  mathematicians  were  all  agreed  in  rejecting  the 
notion  of  an  infinite  number.  As  Amal  remarks,^^  "  All  the 
mathematicians  who  had  weighed  the  terms  of  the  alternative 
.  .  .  were  unanimous.  All  from  Galileo  to  Cauchy  had  em- 
phasized the  impossibility  of  the  infinite  of  quantity,  the  ab- 
surdity of  the  realized  infinite.  .  .  .  Why  should  that  which 
is  impossible  and  absurd  from  the  point  of  view  of  mathematics 
be  maintained  from  the  point  of  view  of  metaphysics  ? " 

Since  the  middle  of  the  last  century,  however,  the  math- 
ematicians have  been  more  favorably  disposed  towards  the 
quantitative  infinite,  and  the  neo-criticists'  appeal  to  the  con- 
sensus of  all  mathematicians  "  from  Galileo  to  Cauchy  "  is  met 
by  the  counter-appeal  to  a  rival  consensus  of  philosophical 
mathematicians  and  mathematically-minded  philosophers 
from  Bolzano  to  Bertrand  Russell.  In  the  judgment  of  sev- 
eral contemporary  thinkers  one  of  the  great  achievements  of 
the  latter  half  of  the  nineteenth  century  was  the  discovery  of  a 
new  definition  of  infinity,  which,  it  is  maintained,  frees  the 
conception  from  all  the  difficulties  and  puzzles  found  in  it  as 
formerly  defined. 

1.  The  New  Definition  of  Infinity. — The  "  new  "  definition 
of  infinity  is  an  incident,  perhaps  the  culminating  incident, 
in  the  "generalization"  of  the  concept  of  number.'''^  If  we 
had  only  the  finite  whole  numbers,  1,  2,  3,  etc.,  while  the  fun- 
damental operations  of  addition,  multiplication,  and  involu- 
tion would  be  in  every  case  possible,  the  inverse  operations 
would  not  be  universally  possible.  For  example,  it  would  be 
impossible,  if  we  had  only  such  numbers,  to  subtract  3  from 

70  La  Philosophie  religieuse  de  Charles  Benouvier,  p.  36. 
'iCouturat,  De  L'Infini  Mathematiqiie,  pp.  5-68,  281. 

50 


Theology  and  the  ''New  Infinite/*  61 

2,  to  divide  2  by  3,  or  to  find  the  square  root  of  3.  In  order 
that  subtraction,  division,  and  evolution  may  be  universally 
possible,  mathematicians  have  introduced  the  conception  of 
negative  numbers  and  zero,  of  fractional  numbers,  and  of 
irrational  and  imaginary  numbers.  The  definition  of  infinite 
or  "transfinite"  numbers  should  therefore  be  considered,  not 
as  an  isolated  incident,  but  as  a  part  of  this  larger  movement 
of  mathematical  thought. 

One  of  the  discoverers  of  transfinite  number  was  Georg 
Cantor.  His  theory  of  number  is  found  in  two  memoirs  which 
appeared  in  the  Mathematische  Annalen  for  1895  and  1897 
under  the  title  '' Beitrdge  zur  Begrilndung  der  Transfiniten 
Mengenlehre.^^  These  memoirs  have  been  translated  into  Eng- 
lish by  Philip  E.  B.  Jourdain  under  the  title  of  "  The  Theory 
of  Transfinite  Numbers/''^  ^  Cantor  here  defines  the  "  power  " 
or  "  cardinal  number  "  of  an  aggregate  M  as  "  the  general  con- 
cept which,  by  means  of  our  active  faculty  of  thought,  arises 
from  M  when  we  make  abstraction  of  the  nature  of  its  various 
elements  m  and  of  the  order  in  which  they  are  given."  If  we 
do  not  make  abstraction  of  the  order,  but  only  of  the  nature 
of  the  elements,  the  resulting  concept  is  the  ordinal  number  of 
the  aggregate  M,  Two  aggregates  are  equivalent,  and  there- 
fore have  the  same  cardinal  number,  "if  it  is  possible  to  put 
them,  by  some  law,  in  such  a  relation  to  one  another  that  to 
every  element  of  each  one  of  them  there  corresponds  one  and 
only  one  element  of  the  other."^*  Employing  the  notions  of 
an  aggregate  and  of  equivalence,  together  with  the  notions  of 
"bindings"  and  "coverings,"  Cantor  then  defines  the  con- 
cepts of  "greater"  and  "less,"  and  the  operations  of  addi- 
tion, multiplication,  and  involution.''* 

72  The  Open  Court  Publishing  Company,  1915. 

73  The  Theory  of  Transfinite  Numbers,  p.  86. 

"f^Ibid.,  pp.  89-95.  One  aggregate  is  said  to  be  greater  than  another 
(and  therefore  the  cardinal  number  of  the  first  greater  than  the  cardinal 
number  of  the  second)  when  (a)  there  is  a  part  of  the  first  which  is 
equivalent  to  (i.  e.,  can  be  put  in  one-to-one  correspondence  with)  the 
second,  but  (ft)  no  part  of  the  second  which  is  equivalent  to  the  first  (pp. 
89  ff.). 


52  The  Argument  for  a  Finitist  Theology, 

This  brings  him  to  the  discussion  of  the  finite  and  trans- 
finite  numbers.  ^^  Aggregates  with  finite  cardinal  numbers," 
he  says,  "  are  called  '  finite  aggregates ' ;  and  all  others  we 
call  Hransfinite  aggregates/  and  their  cardinal  numbers 
'transfinite  cardinal  numbers.' ''^^  The  transfinite  numbers 
are  thus  those  that  are  not  finite.  We  must  therefore  seek  the 
distinguishing  mark  of  the  finite  number.  This  is  to  be  found 
in  the  following  theorem :  "  If  ilf  is  an  aggregate  such  that  it 
is  of  equal  power  with  none  of  its  parts,  then  the  aggregate 
(M,  e),  which  arises  from  M  by  the  addition  of  a  single  new 
element  e,  has  the  same  property  of  being  of  equal  power  with 
none  of  its  parts."  This  theorem  is  used  in  establishing  the 
fundamental  properties  of  the  "unlimited  series  of  finite  car- 
dinal numbers,"^^  and  becomes  a  virtual  part  of  their  defini- 
tion. Finite  aggregates,  accordingly,  are  never  equivalent  to 
any  of  their  parts,  while  transfinite  aggregates  may  be.  "  The 
first  example  of  a  transfinite  aggregate,"  continues  Cantor, 
"  is  given  by  the  totality  of  finite  cardinal  numbers ;  we  call 
its  cardinal  number  *  Aleph-zero.' "  The  first  transfinite  cai^ 
dinal  number  is,  then,  the  cardinal  number  of  the  "  totality  " 
of  finite  cardinal  numbers.''''^ 

It  should  be  noted  that  Cantor  calmly  assumes  the  logical 
tenability  of  this  notion  of  the  "totality"  of  an  unlimited 
series,  and  as  we  shall  presently  see  this  is  the  crux  of  the 
whole  matter.  Just  now,  however,  it  is  our  purpose  to  under- 
stand the  doctrine  rather  than  to  criticize  it. 

A  further  advance  in  the  theory  of  number  ought  next  to  be 
noted.  Cantor,  as  we  have  seen,  defined  "  cardinal  number " 
and  "ordinal  type"  as  "general  concepts  which  arise  by 
means  of  our  mental  activity."  Frege,  in  his  Grundlagen  der 
Arithmetih  of  1884,  defined  "the  number  of  a  class  u"  as  "the 
class  of  all  these  classes  which  are  equivalent  to  u.^^  The  same 
definition  was  discovered  independently  by  Bertrand  Russell. 
"  The  two  chief  reasons  in  favor  of  this  definition,"  says  Jour- 

f^Ihid.,  p.  103. 
76  Hid.,  pp.  97-103. 
fTlhid.,  p.  103. 


Theology  and  the  "New  Infinite/'  53 

dain,  "are  that  it  avoids,  by  a  construction  of  ^numbers'  out 
of  the  fundamental  entities  of  logic,  the  assumption  that  there 
are  certain  new  and  undefined  entities  called  ^  numbers  ^ ;  and 
that  it  allows  us  to  deduce  at  once  that  the  class  defined  is  not 
empty,  so  that  the  cardinal  number  u  exists  in  the  sense  de- 
fined in  logic;  in  fact,  since  u  is  equivalent  to  itself,  the  car- 
dinal number  of  u  has  u  at  least  as  a  member."^®  Cantoris 
definition  of  an  infinite  or  transfinite  number  accordingly  be- 
comes "the  class  of  all  classes  that  are  similar  to  parts  of 
themselves.  ""^^ 

The  "New  Infinite"  was  independently  discovered  by 
Richard  Dedekind.®^  His  definition  runs  as  follows :^^  "A 
system  8  is  said  to  be  infinite  when  it  is  similar  to  a  proper 
part  of  itself;  in  the  contrary  case,  8  is  said  to  be  a  finite 
system." 

The  words  "system,"  "similar,"  and  "proper  part"  are 
employed  in  a  technical  sense,  and  require  some  explanation. 
A  collection  of  objects  is  called  a  system  (also  by  different 
writers  an  aggregate,  manifold,  or  set)  when  it  fulfils  the  fol- 
lowing conditions:®^ 

(1)  It  includes  all  the  objects  to  which  a  definite  quality 
belongs. 

(2)  It  includes  no  object  which  does  not  possess  this 
quality. 

(3)  Each  of  the  included  objects  is  permanently  the  same, 
and  distinct  from  all  the  others.  These  separate  objects  are 
called  elements.  In  Dedekind's  terminology,  every  system  is 
a  part  of  itself;  while  a  system  which  contains  some,  but  not 
all,  of  the  elements  of  a  given  system  is  a  proper  part  of  the 
given  system.  The  notion  of  similarity  is  identical  with  Can- 
tor's "equivalence,"  and  exactly  the  same  meaning  is  con- 

T8  Ihid.,  pp,  202  f . 

7»  Russell,  Principles  of  Mathematics,  pp.  262,  3'21. 

90  Essays  on  the  Theory  of  Numhers,  p.  41.  This  is  a  translation  by 
W.  W.  Beman  of  Dedekind's  papers  on  '  *  StetigJceit  und  irrationale 
Zahlen ' '  and  *  *  Was  sind  und  was  sollen  die  Zahlen. ' ' 

8i76i^.,  p.  63. 

82  Cf.  Encyclopedia  Britannica,  1910,  Article  on  Number. 


54  The  Argument  for  a  Finitist  Theology. 

veyed  by  the  phrase  "one-to-one  correspondence."  Any  two 
groups  or  series  are  said  to  stand  to  each  other  in  the  relation 
of  one-to-one  correspondence  when  for  each  element  or  term 
of  the  one  there  is  one  and  only  one  element  or  term  of  the 
other,  and  vice  versa.  To  borrow  an  illustration  from  Mr, 
Kussell,^^  "  The  relation  of  father  to  son  is  called  a  one-many 
relation,  because  a  man  can  have  only  one  father  but  may  have 
many  sons;  conversely,  the  relation  of  son  to  father  is  called 
a  many-one  relation.  But  the  relation  of  husband  to  wife  (in 
Christian  countries)  is  called  one-one,  because  a  man  cannot 
have  more  than  one  wife,  or  a  woman  more  than  one  husband." 

Dedekind's  point  is  not  that  two  systems  which  are  assumed 
or  already  known  to  be  infinite  are  similar  or  one-to-one  corre- 
spondent, even  if  the  one  is  only  a  part  of  the  other.  That 
such  a  similarity  or  equivalence  is  to  be  found  between  whole 
and  part  was,  as  we  have  seen,  the  very  puzzle  that  had  per- 
plexed the  older  mathematicians.  The  achievement  of  Dede- 
kind  (if  it  is  a  genuine  achievement)  is  rather  the  reversal  of 
the  method  of  attack.  The  "  similarity  "  of  whole  and  part  is 
no  longer  merely  an  observed  fact,  nor  is  it  for  him  an  inr 
ference  from  their  infinity;  but  infinity  is  now  defined  to  he 
such  similarity.  If  a  system  or  aggregate  is  similar  to  a  proper 
part  of  itself,  then  it  is  infinite;  and  this  is  the  definition  of 
an  infinite  system. 

2.  The  New  Infinite  and  Logical  Finitism. — It  has  been 
maintained  by  M.  Couturat  and  others  that  Kenouvier's 
critique  of  infinite  number,  and  therefore  his  whole  system  of 
philosophy  so  far  as  it  is  based  upon  this  critique,  is  founded 
upon  an  erroneous  definition  of  the  mathematical  infinite.^* 
It  accordingly  becomes  a  matter  of  some  importance  to  inquire 
into  the  merits  of  this  "new"  and,  as  is  maintained,  more 
correct  definition.  Our  examination  will  lead  us  to  the  con- 
clusion that  the  "new"  infinite  is  only  the  old  infinite  in  a 
rather  easily  penetrable  disguise;  that  the  definition  of  Dede- 

83  Scientific  Method  in  Philosophy,  p.  203. 
8*Pe  L'Infini  Mathematique,  pp.  444 ff. 


Theology  and  the  ''New  Infiniie/'  56 

kind  and  Cantor  is  the  logical  equivalent  of  the  definition  sug- 
gested by  etymology;  that,  therefore,  if  the  reasoning  of  the 
neo-criticists  is  sound  as  long  as  we  use  the  old  definition,  their 
arguments  lose  none  of  their  cogency  when  we  substitute  the 
definition  formulated  by  the  new  school  of  mathematicians. 

If  we  had  no  other  preceptor  than  etymology,  we  should  at 
once  conclude  that  the  infinite  is  that  which  is  limitless  or  in- 
capable of  completion.  The  definition  of  infinity  adopted  by 
Kant  in  his  account  of  the  "  First  Conflict  of  the  Transcenden- 
tal Ideas"  appears  to  be  no  more  than  an  elaboration  of  this 
notion  of  Unendlichheit.  "  The  infinity  of  a  series,"  he  says, 
"  consists  in  this,  that  it  can  never  be  completed  by  means  of 
a  successive  synthesis."  Or  again,  "  The  true  transcendental 
concept  of  infinity  is,  that  the  successive  synthesis  of  units 
in  measuring  a  quantity  can  never  be  completed."^^  For  Kant, 
then,  the  infinite  is  simply  and  literally  the  endless. 

Another  definition  which  is  of  considerable  historical  im- 
portance is  that  of  Bolzano.  Professor  Keyser  paraphrases  it 
as  follows  :^^  "  Suppose  given  a  class  C  of  elements.  Out  of 
these  suppose  a  series  is  formed  by  taking  for  first  term  one 
of  the  elements,  for  second  term  two  of  them,  and  so  on.  Any 
term  so  obtained  is  itself  a  class  of  elements,  and  is  defined  as 
finite.  Now  either  the  process  in  question  will  exhaust  C  or 
it  will  not.  If  it  will,  C  is  itself  demonstrably  finite ;  if  it  will 
not,  C  is  defined  to  be  infinite."  Bolzano  is  recognized  as  the 
initiator  of  the  movement  which  led  to  the  formulation  of  the 
much-heralded  "  New  Infinite " ;  and  Keyser  tells  us  in  the 
article  from  which  the  above  excerpt  has  been  taken  that  Bol- 
zano's definition,  although  perhaps  not  so  convenient  in  the 
actual  practice  of  the  mathematician,  is  in  principle  exactly 
equivalent  to  that  of  Dedekind.  However  this  may  be,  it  is 
clear  that  Bolzano's  definition  is  exactly  equivalent  to  that  of 
Kant.  The  difference  between  the  two  is  formal  only.  Kant 
employs  the  method  of  addition;  Bolzano  that  of  subtraction. 

95  Kritilc  der  Beinen  Vemunft,  A,  426  and  432.  (Mueller's  translation, 
pp.  344,  348.) 

9^  Journal  of  PhUosophy,  etc.,  I,  33. 


66  The  Argument  for  a  Finitist  Theology. 

The  former  is  thinking  of  the  completion  of  a  somewhat  that 
exists  only  as  a  scheme  or  plan ;  the  latter  is  thinking  of  the 
depletion  of  an  already  existing  class  of  elements.  Yet  the 
fundamental  thought  is  the  same  in  both:  that  which  is  in- 
finite is  endless;  and  because  it  is  endless,  it  is  impossible 
either  to  construct  anything  so  great  as  to  equal  it,  or  to  take 
away  from  it  anything  so  great  as  to  exhaust  it. 

Let  us  now  examine  the  "new"  definition  of  infinity  as  it 
has  been  formulated  by  Dedekind.  "  A  system  S  is  said  to  be 
infirdte  when  it  is  similar  to  a  proper  part  of  itself.''  As  a 
first  step  in  my  argument  that  this  infinite  is  only  the  old 
infinite  in  a  new  suit  of  clothes,  I  shall  show  that  whenever  a 
series  is  found  which  is  "  similar  to/'  that  is  to  say,  in  one-to- 
one  correspondence  with,  a  proper  part  of  itself,  the  series  in 
question  may  he  shown  to  he  in  several  other  kinds  of  corre- 
spondence with  the  same  part;  in  fact,  any  sort  of  corre- 
spondence that  one  pleases  to  look  for  may  be  discovered ;  and, 
furthermore,  any  scheme  or  plan  of  correspondence  may  he 
shown  to  he  just  as  rigidly  determined  hy  law  as  any  other — 
and  specifically,  as  the  scheme  of  one-to-one  correspondence, 
which  the  partizans  of  the  "New  Infinite"  have  too  hastily 
assumed  to  be  the  relation  in  which  the  two  series  eternally 
stand. 

Consider  as  a  typical  case  the  series  of  even  numbers, 
which,  by  definition,  is  a  proper  part  of  the  series  of  whole 
numbers,  and  yet  is  required  to  stand  in  one-to-one  corre-; 
spondence  with  that  series,  by  the  law  that  each  of  its  terms  is 
a  number  twice  the  corresponding  term  of  the  series  of  whole 
numbers.  This  series  illustrates  the  "  similarity  "  of  a  system 
to  a  proper  part  of  itself;  and,  therefore,  by  Dedekind's  defi- 
nition, is  infinite.  But  we  find  that  any  other  correspondence 
than  the  one-to-one  may  be  seen,  if  we  wish  to  see  it.  This 
may  be  exhibited  thus : 

(F)     1,     2,     3,     4,      5,       6,      ••• 
"■■      (P)     2,     4,     6,     8,     10,     12,     ••• 


11. 
III. 

IV. 


Theology  and  the  ''New  Infinite/'  57 

{W) 

{P) 

(If) 

{P) 

{W)       1,2,  3,4,  5,6,  7,8, 

(P)     2,4,6,     8,10,12,     14,16,18,     20,22,24. 


1, 

2, 

3,             4, 

5, 

2,4, 

6,8, 

10,12,     14,16, 

18,  20, 

1,2, 

3,4, 

5,6,     7,8,   ••• 

2, 

4, 

6,         8,     ••• 

Case  I  is  the  case  which  has  been  supposed  to  be  the  situ- 
ation. In  the  other  three  cases  we  have  respectively  a  one-to- 
two,  a  two-to-one,  and  a  two-to-three  correspondence.  Now 
these  other  sorts  of  corresipondence  are  determined  by  clear 
and  definite  rules,  of  exactly  the  same  kind  as,  although  a  little 
more  complicated  than,  the  rule  which  determines  the  one-to- 
one  correspondence.  In  Case  II,  let  the  rule  be,  that  the  sec- 
ond of  the  two  terms  paired  with  any  one  term  of  the  whole 
series  shall  be  four  times  that  term ;  in  Case  III  the  second  of 
the  two  terms  of  (W)  is  the  same  number  as  the  one  term  of 
(P)  with  which  the  two  terms  of  (W)  are  bound  up;  in  IV 
every  two  terms  of  (W)  are  bound  up  with  three  of  (P),  and 
the  rule  determining  the  correspondence  is,  that  the  last  term 
of  any  given  group  of  (P)  shall  be  three  times  the  last  term 
of  the  corresponding  group  of  (W).  Now  it  is  necessary  to 
insist  that  the  (P)  of  I,  of  II,  of  III,  and  of  IV  is  exactly 
the  same  series.  The  "proper  part,"  2,  4,  6,  8,  10,  12,  14, 
16,  •••,  is  the  "proper  part"  that  is  considered  in  each  case. 
It  has  been  shown,  then,  that  the  whole  series  stands  to  this 
proper  part  in  these  various  relations  of  correspondence  m 
exactly  the  same  sense  in  which  it  stands  to  it  in  the  relation 
of  one-to-one  correspondence. 

The  proof  that  this  is  true  of  any  proper  part  of  the  series 
of  whole  numbers  that  one  may  choose  to  consider,  as  for  ex- 
ample, the  series  of  multiples  by  3,  4,  etc.,  or  of  squares,  cubes, 
etc.,  of  the  terms  of  the  natural  series  of  numbers,  must  be 
left  to  the  ingenuity  and  patience  of  the  reader.^^     He  will 

87  In  the  typewritten  copy  of  this  dissertation,  which  may  be  found  in 
the  library  of  the  Johns  Hopkins  University,  I  have  considered  these  and 
other  series  in  considerable  detail,  and  have  suggested  formulae  for  several 


68  The  Argument  for  a  Finitist  Theology. 

find  that  the  correspondence  of  a  whole  and  a  proper  part  o£ 
itself,  which  has  been  taken  as  the  essential  notion  in  the 
"new"  definition  of  infinity,  turns  out,  when  more  closely 
scrutinized,  to  be  a  nose  of  wax ;  it  can  be  bent  in  any  direc- 
tion that  one  pleases. 

How  then  shall  we  interpret  Dedekind's  definition,  in  the 
light  of  our  examination  of  these  examples  of  the  relation  of 
one-to-one  correspondence  of  whole  and  part ?  "A  system  S  is 
infinite  if  it  is  similar  to  a  proper  part  of  itself."  Does  this 
mean  (1)  That  the  whole  and  the  proper  part  in  question  are 
in  one-to-one  correspondence,  and  in  no  other,  or  (2)  that  the 
whole  is  in  one-to-one  correspondence  with  a  proper  part  of 
itself,  but  is  also  related  to  the  same  part  in  accordance  with 
other  schemes  of  correspondence? 

If  the  former  interpretation  is  correct,  then,  so  far  as  I  am 
aware,  no  genuine  example  of  an  infinite  system  has  ever  been 
adduced.  At  any  rate,  no  example  of  an  infinite  system  is  re- 
vealed by  an  examination  of  the  mutual  relations  of  the  various 
series  of  cardinal  numbers.  If  this  is  the  meaning  of  the 
definition,  the  class  of  all  classes  each  of  which  is  "  similar " 
to  a  proper  part  of  itself  is  a  class  without  any  members;  for 
we  have  found  that  in  every  case  where  a  one-to-one  corre- 
spondence is  discoverable,  correspondences  of  other  sorts  are 
also  discoverable. 

On  the  other  hand,  if  the  latter  is  understood  to  be  the 
meaning  of  the  definition,  if  the  whole  and  its  proper  part  are 
in  a  relation  of  one-to-one  correspondence,  and  also  in  rela- 
tions of  one-to-two  correspondence,  two-to-three  correspond- 
ence, etc.,  then  the  definition  is  not  new,  but  is  logically  iden- 
tical with  or  at  all  events  necessarily  implies  the  old  definition 
of  the  infinite  as  the  endless;  for  any  endless  series  is  inex^ 
haustihle,  and,  between  two  inexhaustible  collections,  it  is  al- 
ways possible  to  exhibit  a  one-to-one  correspondence,  or  any 
sort  of  correspondence  that  one  chooses  to  look  for,  inasmuch 

types  of  proper  parts,  by  the  use  of  wMcli  an  "m-to-n.  correspondence ' ' 
(m  and  n  being  any  whole  numbers)  may  be  determined  between  the 
series  of  whole  numbers  and  any  given  proper  part. 


Theology  and  the  "New  Infinite/'  59 

as,  however  far  the  pairing  of  terms  or  the  correlation  of 
groups  may  be  carried,  there  can  never  be  any  dearth  of  part- 
ners or  of  groups  of  terms  in  either  collection. 

We  should  expect,  then,  that  the  logical  absurdity  found  by 
Renouvier  in  the  conception  of  a  "realized  infinite"  would 
not  be  removed  by  so  simple  an  expedient  as  the  re-phrasing 
of  the  definition  of  infinity.  The  creators  of  the  "  E"ew  In- 
finite "  have  indeed  "  taken  the  bull  by  the  horns,"^^  and  have 
sought  to  escape  the  self-contradiction  lurking  in  the  notion 
of  infinity  by  making  this  very  self-contradiction  the  heart 
and  center  of  their  definition.  But  this  does  not  remove  the 
contradiction.  Although  it  has  been  sugar-coated,  it  is  still 
there ;  and  it  is  an  obvious,  though  not  infrequently  neglected, 
logical  requirement  that,  to  quote  the  words  of  Poincare,  "  in 
defining  an  object  we  affirm  that  the  definition  does  not  imply 
a  contradiction.''^^ 

Now  when  Dedekind  speaks  of  the  endless  series  of  cardinal 
numibers  as  a  system,  he  tacitly  imports  the  notion  of  finitude 
into  his  definition  of  infinity.  For  we  naturally  think  of  a 
system  as  a  whole,  a  somewhat  that  is  completely  given.  The 
self-contradiction  appears  even  more  clearly  when  we  consider 
the  phraseology  of  Cantor.  His  "  infinite  aggregate  "  is  con- 
ceived as  a  "  totality."  Thus  his  first  example  of  an  infinite 
or  transfinite  aggregate  is  the  "  totality  of  finite  cardinal  num- 
bers."^^  But  as  he  himself  speaks  of  "the  unlimited  series 
of  cardinal  numbers,"^^  it  is  clear  that  he  has  fallen  into  a 
self-contradiction,  or  else  that  in  his  usage  the  term  "  totality  " 
is  not  to  be  understood  in  the  same  sense  as  in  the  arguments 
of  the  neo-criticist  school.  For,  if  the  series  of  numbers  is 
unlimited,  what  right  have  we  to  speak  of  it  as  a  whole  or  a 
totality 9  If  the  word  "totality"  is  understood  in  the  sense 
in  which  it  is  employed  by  Renouvier  and  Pillon,  its  use  in  a 
definition  of  the  number  "Aleph-zero"  would  constitute  a 

88  James,  Problems  of  Philosophy,  p.  176, 

89  Science  et  MSthode,  p.  162. 

90  The  Theory  of  Transfinite  Numbers,  p.  103. 

91  Ibid.,  p.  99. 


60  The  Argument  for  a  Finitist  Theology, 

begging  of  the  whole  question  which  is  at  issue  between  the 
finitists  and  the  infinitists.  If,  however,  when  Cantor  speaks 
of  a  "totality,"  he  means  no  more  than  that  the  collection  or 
series  which  he  denotes  by  the  term  is  determinate  (that  is,  is 
so  defined  that  it  is  in  principle  possible  to  distinguish  it  from 
every  other  collection  or  series  and  always  possible  to  tell 
whether  or  not  it  includes  any  given  term  or  collection  of 
terms),  then  such  a  "totality"  may  be  infinite  in  the  old 
sense,  that  is  to  say,  it  may  be  endless.  For  example,  we  can 
always  tell  whether  or  not  a  given  number  belongs  to  the  series 
of  even  numbers  or  to  the  series  of  odd  numbers;  and,  inas- 
much as  these  series  are  thus  logically  distinguishable,  there 
is  a  sense  in  which  they  are  definite  and  thinkable  unities; 
yet  each  of  these  series  is  endless,  because,  by  the  very  law  of 
its  formation,  however  far  it  is  continued,  we  must  needs  look 
for  more  and  still  more  terms.  Such  determinate  but  endless 
series  are,  indeed,  examples  of  Renouvier's  "  indefinite."  But 
in  Renouvier's  terminology  an  "endless  totality"  would  be  a 
contradiction  in  terms.  That  is  why  a  "  realized  infinite  "  is 
logically  impossible.  An  infinite  that  was  realized,  a  some- 
what actually  existing  and  not  merely  a  scheme  or  plan  in 
process  of  realization,  would  be  a  totality  in  the  sense  that  no 
part  of  it  would  be  wanting;  and  yet  as  infinite  it  would  be 
endless  or  unfinished. 

There  may  be,  and  no  doubt  are,  many  logically  distinguish- 
able types  of  endless  series;  and  accordingly  it  is  perfectly 
legitimate  for  the  mathematician  to  study  these  various  types, 
and  even  to  call  them  transfinite  numbers  if  he  wishes  to  em- 
ploy that  terminology,  and  is  not  himself  led  astray  by  it. 
But  unless  we  forget  this  ambiguity  in  the  meaning  of  the 
term  "  totality,"  it  is  impossible  to  suppose  that  the  definition 
of  "  transfinite  number  "  has  made  any  contribution  whatever 
toward  the  solution  of  the  logical  difficulty  found  by  the  school 
of  Renouvier  in  the  conception  of  a  "  realized  infinite." 

3.  The  New  Infinite  and  Monistic  Idealism. — ^We  must 
next  inquire  what  bearing,  if  any,  these  recent  discussions  of 


Theology  and  the  "New  Infinite/'  61 

the  definition  of  infinity  have  upon  the  doctrine  of  the  monistic 
Absolute.  Monistic  idealism,  I  have  said,  implies  the  con- 
ception of  infinity  in  both  senses.  In  our  second  chapter  we 
saw  that  God  cannot  be  conceived  without  contradiction  to  be 
infinite  in  the  first  sense — he  cannot  be  regarded  as  including 
all  reality ;  and  now  it  is  in  order  to  consider  the  dependence 
of  monistic  idealism  upon  the  notion  of  infinity  in  the  second 
sense — upon  the  mathematical  or  numerical  infinite.  There 
are  two  ways  in  which  monistic  idealism  implies  the  notion  of 
a  realized  infinite: 

{a)  The  Absolute  is  said  to  be  in  possession  of  all  time  in 
an  Eternal  Now,  "  The  real  world  of  our  Idealism  has  to  be 
viewed  by  us  men  as  a  temporal  order.  For  it  is  a  world  where 
purposes  are  fulfilled.  .  .  ."  But  "this  same  temporal  order 
is,  when  regarded  in  its  wholeness,  an  Eternal  Order.  .  .  . 
The  whole  real  content  of  this  temporal  order  ,.,  is  at  once 

known,  i.  e.,  is  consciously  experienced  as  a  whole,  by  the  Ab- 
solute."92 

This  may  perhaps  mean  that  the  temporal  order  is  an  "  il- 
lusion of  the  partial  view,"  that  it  belongs  to  the  realm  of  mere 
appearance  and  not  to  that  of  genuine  reality.  We  have 
already  pointed  out  the  difficulty  of  attaching  any  meaning  to 
the  proposition  that  time  is  illusory,^^  and  need  not  repeat 
what  has  already  been  said.  The  sentences  just  quoted  from 
Professor  Royce  are  capable  of  another  interpretation.  When 
he  says  that  the  whole  content  of  the  temporal  order  is  known 
at  once,  he  himself  explains  the  phrase  at  once  as  equivalent 
to  in  the  same  present,  Now  the  present,  he  tells  us,  is  some- 
times understood  to  be  the  mathematical  line  which  separates 
the  future  and  the  past,  and  as  a  mere  boundary  to  be  without 
extent.  Again  the  present  "  is  any  one  temporal  event,  in  so 
far  as  it  is  contrasted  with  antecedent  and  subsequent  events, 
and  in  so  far  as  it  excludes  them  from  coexistence  with  itself 
in  the  same  portion  of  any  succession."     In  the  third  place, 

s^Boyce,  The  World  and  the  Individual,  II,  134  and  138. 
»3  Chapter  II,  Section  2  (6). 


62  The  Argument  for  a  Finitist  Theology. 

the  present  "  is  any  portion  of  real  time  with  all  its  included 
events,  in  so  far  as  there  is  any  reason  to  view  it  as  a  whole, 
and  as  known  in  this  wholeness  by  a  single  experience."^* 
When  Koyce  says,  then,  that  the  whole  temporal  order  is 
known  ai  once,  his  meaning  ma/y  he  no  more  than  that  the 
whole  temporal  order  is  a  whole.  All  time 'is  present  to  the 
Absolute  as  a  totum  simuU^ 

Here,  however,  we  meet  the  difficulty  of  the  realized  in- 
finite, of  the  totality  of  the  unlimited.  Royce  seeks  to  justify 
the  conception  of  the  totum  simul  by  regarding  it  as  analogous 
to  the  "specious  present"  of  the  individual  mind.  We  per- 
ceive the  words  of  a  phrase  or  a  brief  clause  like  "  The  curfew 
tolls  the  knell  of  parting  day,"  not  merely  as  successive,  but 
also  all  at  once,  as  a  whole.  In  the  same  way  the  Absolute, 
thinks  Royce,  knows  all  the  events  of  all  time  at  once  or  as  a 
whole.  Many  questions  might  be  asked  about  the  analogy  of 
the  "  specious  present "  and  the  "  totum  simul."  But  we  can 
not  ask  them  here.  I  merely  wish  to  stress  the  point  that  the 
idealistic  doctrine  of  an  Eternal  l^ow  must  stand  or  fall  with 
the  logical  possibility  or  impossibility  of  the  realized  infinite. 
For  all  time  includes  the  unlimited  past  and  the  unlimited 
future ;  and  how  can  that  which  is  unlimited  be  a  whole  ?^^ 

(&)  The  argument  for  monistic  idealism  depends  upon  the 
assumption  that  a  thing  exists  "just  in  so  far  as  there  is  ex- 
perience of  its  existence."^'''  This  principle  is  a  special  appli- 
cation of  the  more  general  principle  of  the  "intemality  of 
relations."  If  a  "thing"  is  constituted  by  the  relations  in 
which  it  stands,  then  the  attempt  to  define  anything  must  in- 
evitably lead  to  an  infinite  regress ;  and  the  infinite  regress  is 
logically  intolerable.  This  is  the  burden  of  Mr.  F.  H.  Brad- 
ley^s  ^^  Appearance  and  Reality.''  The  attempt  to  define  any 
of  the  ordinary  categories  of  thought,  as  substance,  quality, 

9*  The  World  and  the  Individual,  11,  140. 

95  ihid.,  p.  141. 

96  Compare  Chapter  V,  Section  2. 

97  The  Conception  of  God,  p.  43. 


Theology  and  the  ''New  Infinite/'  63 

relation,  the  self,  etc.,  brings  us  to  no  final  or  satisfactory  con- 
clusion, but  merely  produces  an  endless  series. 

Critics  of  a  realistic  temper  may  cut  the  knot  by  denying 
the  principle  of  the  internality  of  relations.  Royce,  however, 
is  committed  to  this  principle,  and  therefore  seeks  to  avoid  the 
difficulty  by  maintaining  that  the  "  infinite  regress "  is  not  a 
fatal  defect.  It  is  fatal,  he  holds,  only  when  you  take  it  term 
by  term,  i.  e.j  successively;  if  you  assume  the  infinite  multi- 
tude or  series  of  terms  to  be  given  all  at  once  in  one  single 
purpose  or  plan,  the  infinity  becomes  harmless. 

How  then  is  it  possible  to  take  the  "  infinite  regress  "  all  at 
once?  The  problem,  thinks  Royce,  is  solved  for  us  in  Dede- 
kind's  definition  of  infinity.  Thus  the  'New  Infinite  becomes 
a  main  support  of  monistic  philosophy.  Idealism  implies  an 
infinite  system,  and  the  discovery  of  Dedekind  permits  us  to 
think  of  the  infinite  not  merely  as  endless  but  as  an  instance 
of  self-representation,  "Whatever  considerations  make  for 
an  idealistic  interpretation  of  reality,  become  considerations 
which  also  tend  to  prove  that  the  universe  is  an  infinitely 
complex  reality,  or  that  a  certain  infinite  system  of  facts  is 
real.  For  idealism,  in  defining  the  Being  of  things  as  neces- 
sarily involving  their  existence  for  some  form  of  knowledge, 
is  committed  to  the  thesis  that  whatever  is,  is  ipso  facto  known 
(e.  g.,  to  the  Absolute).  .  .  .  Since,  however,  the  fact  world 
even  for  idealism  contains  many  aspects  (such  as  the  aspects 
called  feeling,  will,  worth,  and  the  like)  which  are  not  iden- 
tical with  knowledge,  although  for  an  idealist  they  all  exist 
as  known  aspects  of  the  world,  it  follows  that  for  an  idealist 
the  facts  which  constitute  the  existence  of  knowledge  are 
themselves  but  a  part  and  not  the  whole  of  the  world  of  facts ; 
yet,  by  hypothesis,  this  part,  since  it  contains  acts  of  knowl- 
edge corresponding  to  every  real  fact,  is  adequate  to  the  whole, 
or  in  Dedekind's  sense  is  equal  to  the  whole.  Hence  the 
idealist's  system  of  facts  must,  by  Dedekind's  definition,  be 
infinite;  or  for  the  idealist  the  real  world  is  a  self-represen- 
tative system,  and  is  therefore  infinite."^^ 

»s  Ihid.,  40. 


64  The  Argument  for  a  Finitist  Theology. 

Moreover,  if  we  try  "  to  conceive  .  .  .  the  universe  in  real- 
istic terms  as  a  realm  v^^hose  existence  is  supposed  to  be  inde- 
pendent of  the  mere  accident  that  anyone  does  or  does  not 
know  or  conceive  it,  .  .  .  it  is  possible  to  show  that  this  sup- 
posed universe  has  the  character  of  a  self-representative  sys- 
tem,'' that  is  to  say,  is  infinite.  For,  "  if  the  supposition  is 
itself  a  fact,  then>  at  that  instant,  when  the  supposition  is 
made,  the  world  of  Being  contains  at  least  two  facts,  namely, 
F  and  your  supposition  about  i^."  Call  the  supposition  /. 
Then  your  universe  is  at  least  F  -{- f.  But,  "  this  universe  as 
thus  symbolized,  has  not  merely  a  twofold,  but  a  threefold  con- 
stitution. It  consists  of  F  and  of  f,  and  of  their  +?  ^-  ^'^^  ^^ 
the  relation  as  real  as  both  of  them,  which  we  try  to  regard  as 
non-essential  to  the  being  of  either  of  them,  but  which  for  that 
very  reason,  has  to  be  supposed  wholly  other  than  themselves, 
just  as  they  are  supposed  to  be  different  from  each  other."^^ 

"  Hereupon,  of  course,  Mr.  Bradley's  now  familiar  form  of 
argument  enters  with  its  full  rights  .  .  .  the  -j-  is  linked  to 
/  and  to  F  and  the  ^endless  fission'  unquestionably  ^break:s 
out/  The  relation  itself  is  seen  entering  into  what  seem  new 
relations."i<^^ 

Thus  Koyce  agrees  with  Bradley  that  every  form  of  real- 
istic being  "  involves  such  endless  or  self-representative  con- 
stitution "  ;^^^  that,  in  particular,  realistic  being  breaks  down 
upon  the  contradictions  resulting  from  this  constitution. 
Royce,  however,  does  not  accept  the  view  "that  to  be  self- 
representative  is  as  such  to  be  self-contradictory."  This  con- 
clusion, he  thinks,  is  obviated  by  the  help  of  the  definition  of 
infinity  as  a  self-representative  system.  The  notion  of  "self- 
representation"  permits  us  to  take  an  infinite  multiplicity  all 
at  once. 

Royce  illustrates  his  meaning  in  various  ways.  Some  manu- 
facturers have  ingeniously  used  a  picture  of  the  package  in 
which  their  product  is  contained  as  a  trade-mark,  and  have 

99  The  World  and  the  Individual,  p.  538  f . 
loojfetU,  p.  540. 
101  JMd.,  p.  542. 


Theology  and  the  ''New  Infinite."  66 

then  placed  this  trade-mark  as  a  label  upon  the  package.  But 
the  package  thus  labeled  with  its  own  picture,  inevitably  re- 
quires the  picture  to  contain  for  accuracy's  sake  ...  a  pic- 
ture of  itself. "^^^  Or  suppose  that  somewhere  upon  the  soil 
of  England  there  is  a  map  of  England.  Suppose,  further, 
that  this  map  is  a  perfect  representation,  indicating  every  de^ 
tail  of  the  surface  of  England.  It  is  clear  that  this  map  must 
contain  a  map  of  itself. 

The  attempt  actually  to  construct  an  accurate  picture  or  a 
perfect  map  of  the  sort  just  described  would  indeed  require 
an  endless  process  and  therefore  be  impossible  of  fulfilment; 
but,  says  Royce,  the  plan  itself  is  given  all  at  once.  "  Math- 
ematically regarded  the  endless  series  of  maps  within  maps, 
if  made  according  to  such  a  projection  as  we  have  indicated, 
would  cluster  about  a  limiting  point,  whose  position  would  be 
exactly  determined.  Logically  speaking  their  variety  would 
be  a  mere  expression  of  the  single  plan,  *  Let  us  make  within 
England  and  upon  the  surface  thereof,  a  precise  map,  with  all 
the  details  of  the  contour  of  its  surface.'  .  .  .  The  one  plan 
of  mapping  in  question  necessarily  implies  just  this  infinite 
variety  of  internal  constitution.  .  .  .  We  are  not  obliged  to 
deal  solely  with  processes  of  construction  as  successive  in  order 
to  define  endless  series."^^^  "  To  conceive  the  true  nature  of 
the  infinite,  we  have  not  to  think  of  its  vastness,  or  even  nega- 
tively of  its  endlessness;  we  have  merely  to  think  of  its  self- 
representative  character."^^^ 

Does  this  idea  of  "self-representation"  escape  the  dif- 
ficulty of  the  "  endless  regress  "  ?  The  issue  thus  raised  is  in 
principle  the  same  as  that  involved  in  the  conception  of  the 
"totality"  of  an  unlimited  series;  yet  inasmuch  as  we  have 
taken  Professor  Royce  as  the  typical  exponent  of  monistic 
idealism  it  seems  proper  to  devote  a  few  paragraphs  to  a  dis- 
cussion of  the  illustration  which  he  himself  employs.  "A 
map  of  England,  contained  within  England,  is  to  represent 

102  The  World  and  the  IndividuaL,  pp.  506  f . 
108  Eibhert  Journal,  I,  35. 


66  The  Argument  for  a  Finitist  Theology. 

down  to  the  smallest  detail  every  contour  and  marking,  natural 
or  artificial,  that  occurs  upon  the  surface  of  England."^^*  The 
perfection  of  the  map  requires  that  there  be  a  "one-to-one 
correspondence,  point  for  point,  of  the  surface  mapped  and 
the  representation."  In  other  words,  if  A  is  the  surface 
mapped  and  A'  the  representation,  "for  every  elementary  de- 
tail of  A,  namely,  a,  h,  c,  d  (be  these  details  conceived  as  points 
or  merely  as  physically  smallest  parts;  as  relations  amongst 
the  parts  of  a  continuum,  or  as  relations  amongst  the  units  of 
a  mere  aggregate  of  particles),  some  corresponding  detail,  a', 
&',  c',  d%  could  be  identified  in  A\  in  accordance  with  the 
system  of  projection  used." 

Let  us  consider  first  the  notion  of  perfect  representation 
where  the  copy  is  assumed  to  be  smaller  than  the  original,  and 
then  that  of  perfect  seZ/-representation. 

In  the  opinion  of  Royce,  "  that  a  smaller  picture  should  be 
a  perfect  representation  of  a  larger  object  is  a  perfectly  de- 
finable ideal."^^^  But  that,  even  as  an  ideal,  it  is  not  a  self- 
contradictory  conception  is  by  no  means  clear.  If  only  de- 
tails that  are  visible  to  the  naked  eye  are  pictured,  there  is  no 
difficulty ;  for  a  microscope  may  be  used  to  read  the  map.  But 
if  the  object  to  be  pictured  is  itself  viewed  under  the  micro- 
scope, and  all  the  details  thus  visible  are  to  be  represented,  it 
is  clear  that  if  the  map  or  picture  were  much  smaller  than  the 
original,  exact  legible  representation  would  be  impossible.  If 
now  it  be  replied,  as  Royce  would  perhaps  reply,  that  the 
quality  of  being  legible  is  irrelevant  to  the  notion  of  perfect 
mapping,  that  all  that  is  meant  by  it  is,  that  for  every  detail 
of  the  original  there  shall  be  a  corresponding  detail  in  the 
copy,  then  it  is  clear  that,  if  both  original  and  copy  are  as- 
sumed to  be  made  up  of  a  finite  number  of  indivisible  units, 
such  perfect  mapping  is  impossible,  unless  the  copy  be  as- 
sumed to  possess  a  finer  texture  than  the  original  (i,  e.,  to 
contain  a  greater  number  of  indivisible  units  to  the  square 

104  World  and  Individual,  I,  503  ff. 

105  Hihhert  Journal,  1,  27. 


Theology  and  the  ''New  Infinite/'  67 

inch).  If,  however,  there  is  assumed  to  be  no  difference  in 
texture,  the  points  or  ultimate  units  of  which  the  material  of 
the  map  or  picture  is  composed  must  be  infinitely  numerous. 

In  other  words,  the  perfect  representation  of  any  object  on 
a  smaller  scale  implies,  either  that  the  copy,  although  smaller, 
contains  exactly  as  many  ultimate  units  as  the  original,  or 
else  that  the  copy  is  a  continuum^  or  at  least  a  compact  collec- 
tion of  points.  If  we  assume  the  notion  of  the  continuum, 
there  is,  then,  no  diflSculty  in  the  idea  of  a  perfect  represen- 
tation of  a  larger  by  a  smaller  surface.  Indeed,  if  we  assume 
that  space  is  continuous  or  compact,  such  representation  is  an 
everywhere-present  fact ;  because,  for  every  point  in  a  solid  or 
a  surface,  there  must  then  be  assumed  to  be  a  point  in  any 
other  solid  or  surface,  however  small  the  latter  may  be. 

It  is  clear,  then,  that  the  idea  of  an  absolutely  perfect  repre- 
sentation, even  without  the  added  notion  of  5eZ/-representa- 
tion,  requires  the  conception  of  an  infinite  multiplicity  of  ele- 
ments, unless  we  make  the  above-mentioned  assumption  con- 
cerning the  finer  texture  of  the  material  of  the  copy.  It  is 
indeed  essential  to  Royce's  argument  that  the  map  be  drawn 
upon  the  soil  of  England,  and  therefore  be  an  example  of  self- 
representation ;  but  this  is  not  essential  to  the  idea  of  the  map 
as  an  illustration  of  infinity.  All  that  is  required  is  the  as- 
sumption that  for  every  point  in  the  surface  of  England  there 
shall  be  a  point  on  the  map,  however  small  the  map  is  drawn. 
But  as  I  have  already  remarked,  this  follows  from  the  notion 
of  the  continuum.  If  two  surfaces  are  both  assumed  to  be 
continuous,  then,  however  large  the  one  may  be  and  however 
small  the  other,  for  every  point  in  the  one  there  is  a  point  (or, 
for  that  matter,  and  this  destroys  the  notion  of  a  definite 
representation,  there  are  two,  three,  or  as  many  as  you  please) 
in  the  other.  Instead,  then,  of  supposing  a  map  within  a  map, 
and  so  on  forever,  we  can  just  as  well  suppose  the  original 
map  without  the  loss  of  any  detail  to  become  smaller  and 
smaller  without  limit.  On  either  assumption  the  perfect  map- 
ping, even  of  only  the  visible  markings  of  England's  surface, 


68  The  Argument  for  a  Finitist  Theology. 

would  imply  the  notion  of  an  infinite  multitude  of  points  in 
any  designated  portion  of  the  surface  upon  which  the  map  is 
drawn. 

In  the  case  of  s62/-rep resent ation,  or  rather  of  representa- 
tion by  a  part  of  that  which  is  represented,  it  is  obvious  that 
the  notion  of  infinite  multitude  must  be  assumed ;  for  here  we 
have  representation  on  a  smaller  scale,  and  there  is  no  dif- 
ference in  the  texture  of  the  original  and  the  copy,  or  at  least 
of  part  of  the  original  and  the  copy.  We  find  then  that  we 
have  been  traveling  in  a  circle.  In  an  effort  to  avoid  the  end- 
less regress  we  have  defined  a  conception  of  self-representation, 
only  to  find,  when  we  examine  our  conception  a  little  more 
closely,  that  it  contains  the  very  notion  which  it  was  designed 
to  escape.  If,  then,  the  notion  of  an  endless  regress  is  self- 
contradictory,  that  of  self-representation,  or  of  a  purpose  that 
is  infinitely  rich  in  implications,  is  likewise  self-contradictory. 

We  conclude,  therefore,  that  the  "  discovery "  of  the  so- 
called  ^ew  Infinite  leaves  the  problems  of  theology  exactly  as 
it  found  them ;  and  that  the  apparent  bearing  of  the  new  con- 
ception of  infinity  upon  these  problems  is  the  result  of  ai 
double  use  of  such  terms  as  "  totality "  and  "  equality."^^^ 

106  The  reader  may  be  interested  in  Boyce  's  use  of  the  New  Infinite  to 
explain  the  relation  of  the  Absolute  to  the  Particular  Self  {Bibhert  Jour- 
nal, 1,  44)  and  in  Keyser's  attempt  by  its  aid  to  defend  the  doctrine  of 
the  Trinity  and  that  of  the  divine  omniscience  {The  New  In-finite  and  the 
Old  Theology,  pp.  85  ff.).  It  seems  clear  that  both  writers  are  merely 
playing  on  the  word  equality. 

Professor  Eoyce  suggests  that  *'a  wholly  new  light"  is  thrown  *'upon 
the  possible  relations  of  equality  which,  in  a  perfected  state,  might  exist 
between  what  we  now  call  an  Individual  or  a  Created  Self  and  God  as  the 
Absolute  Self.  Perhaps  a  being,  who,  in  one  sense,  appeared  infinitely 
less  than  God,  or  who  at  all  events  was  but  one  of  an  infinite  number  of 
parts  within  the  divine  whole,  might,  nevertheless,  justly  count  it  not  rob- 
bery to  be  equal  to  God,  if  only  this  partial  being  by  virtue  of  an  im- 
mortal life  or  of  a  perfected  process  of  self-attainment,  received  in  the 
universe  somewhere  an  infinite  expression."  When  we  recall,  however, 
that  to  be  'equal'  here  means  no  more  than  to  be  of  the  same  **Mdchtig- 
Jceit,*'  i.  e.,  to  be  in  the  relation  of  one-to-one  correspondence,  it  is  far 
from  clear  that  the  "infinite  expression"  of  the  partial  being  is  of  any 
spiritual  or  ethical  significance. 


Theology  and  the  *'  New  Infinite/'  69 

Professor  Keyser,  who  is  by  profession  a  mathematician,  tells  us  that 
it  is  a  great  error  to  suppose  that  the  whole-part  axiom  is  universally 
valid.  It  ought  rather  to  be  considered  as  a  ''logical  blade"  which 
divides  the  finite  from  the  infinite.  Some  of  the  difficulties  of  theology, 
Professor  Keyser  assures  us,  have  been  caused  by  assuming  that  this 
axiom  applies  to  infinites. 

Thus  the  doctrine  of  the  Trinity  has  been  pronounced  absurd,  because 
it  implies  that  one  infinite  is  composed  of  three  infinites,  and  that  each  of 
the  three  is  equal  not  only  to  each  of  the  others  but  to  the  whole  which 
they  jointly  constitute.  But  this  objection,  says  Keyser,  erroneously  as- 
sumes that  the  whole-part  axiom  holds  for  infinites.  He  illustrates  the 
logical  possibility  of  the  conception  of  a  One  which  is  also  Three  by 
means  of  the  relation  of  the  number-system  to  certain  of  its  parts.  Let 
M  be  the  manifold  of  all  rational  numbers,  E  of  the  even  numbers,  0 
of  the  odd  numbers,  and  F  of  the  rational  fractions;  then  it  is  evident 
that  E,  0,  and  F  are  proper  parts  of  M;  and  also  that  a  one-to-one  corre- 
spondence is  discoverable  between  M  and  each  of  these  parts  taken  sep- 
arately. Therefore  by  Dedekind's  definition,  M,  E,  0,  and  F  are  all  in- 
finite manifolds.  "What  is  important  is  now  obvious,"  says  Keyser. 
"It  is  that  we  have  here  three  infinite  manifolds,  E,  0,  F,  no  two  of 
which  have  so  much  as  a  single  element  in  common,  and  yet  the  three 
together  constitute  one  manifold  M  exactly  equal  in  wealth  of  elements 
to  each  of  its  infinite  components."  The  application  to  the  theological 
Trinity  is  of  course  evident. 

An  obvious  objection  here  presents  itself.  One  might  naturally  inquire 
why  there  are  just  three  rather  than  two  or  four  persons.  Indeed  the 
mathematical  analogy  suggests  an  infinity,  or  at  least  a  very  large  number, 
of  constituent  persons;  and,  as  we  have  seen,  Royce  holds  that  the  Abso- 
lute may  be  conceived  without  contradiction  to  include  a  multitude,  and, 
in  fact,  an  infinite  multitude,  of  selves.  This  objection,  however,  misses 
Keyser 's  point,  which  is,  not  that  the  doctrine  of  the  Trinity  can  be 
mathematically  demonstrated,  but  merely  that,  if  on  some  other  ground 
we  believe  that  the  One  is  Three  and  the  Three  are  One,  the  conception  is 
not  logically  absurd. 

It  may  be  questioned,  however,  whether  the  aid  thus  so  kindly  prof- 
fered by  Mathesis  to  Theology  will  be  very  enthusiastically  received.  On 
the  one  hand,  Trinitarians  like  Cardinal  Newman,  who  seems  to  have  liked 
the  doctrine  all  the  more  on  account  of  its  incomprehensibility  (see  New- 
man, The  Grammar  of  Assent,  pp.  124  £f.),  may  even  be  disposed  to 
resent  this  attempt  to  make  their  cherished  formula  as  plain  and  clear  as 
the  multiplication  table  or  the  rule  of  three;  for,  if  the  Trinity  is  not  in- 
comprehensible, half  the  merit  of  assenting  to  the  ancient  creeds  will  be 
lost.  On  the  other  hand,  adherents  of  the  "new  theology"  who  still  con- 
sider themselves  Trinitarians  have  learned  to  interpret  the  ancient  for- 
mulae in  such  a  way  as  to  remove  the  contradiction;  and  therefore  do  not 
recognize  the  need  of  a  demonstration  of  the  eoneeivability  of  a  numer- 
ical Trinity  in  Unity. 


70  The  Argument  for  a  Finitist  Theology. 

The  "new''  conception  of  infinity  is  also  employed  by  Professor  Keyser 
in  defense  of  the  doctrine  of  the  divine  omniscience.  Objection  has  fre- 
quently been  made  to  this  doctrine  on  the  ground  that  it  seems  to  abolish 
human  freedom  and  to  make  God  responsible  for  human  sin.  Keyser  sug- 
gests that  we  may  preserve  the  dignity  of  omniscience  while  giving  up 
omniscience  in  the  strict  sense  of  the  term.  Suppose  the  knowledge  of  all 
events  to  include  an  infinite  number  of  knowledge-elements.  Now  suppose 
this  infinite  manifold  to  be  divided  by  a  plane  which  in  our  imaginative 
construction  represents  the  present  instant.  Then  it  is  evident  that  there 
is  a  one-to-one  correspondence  between  the  manifold  of  elements  either  be- 
fore or  behind  this  boundary  and  the  undivided  manifold.  In  other  words, 
the  knowledge  of  the  past  alone  is  just  as  infinite  as  the  knowledge  of 
the  events  of  all  time.  Accordingly,  even  if  God  is  assumed  to  have  no 
knowledge  of  undetermined  future  events,  His  knowledge  is  nevertheless 
infinite;  and,  in  the  phraseology  of  the  partizans  of  the  New  Infinite, 
God  may  still  be  said  to  possess  the  dignity  or  MdchtigJceit  of  omnis- 
cience. The  same  argument  is  easily  made  to  fit  the  case  of  omnipotence 
or  of  omnipresence.  In  an  infinite  world  the  Deity  might  then  be  infinite 
in  knowledge,  power,  etc.,  without  being  omniscient,  omnipotent,  or  omni- 
present. One  may,  however,  be  sufficiently  "tough-minded"  to  inquire 
just  what  is  the  value  of  the  word  * '  infinite ' '  and  the  phrases  '  *  dignity  of 
omniscience,"  etc.?  Certainly  no  one  would  hold  that  merely  to  be  in- 
finitely rich  in  numerical  elements  is  a  quality  which  is  of  any  ethical 
value;  for,  if  it  were,  then  any  portion  of  a  continuum  would  possess  this 
transcendent  dignity. 


VII. 

Concluding  Reflections  on  Finitist  Theology. 

1.  A  Recapitulation  of  the  Argument  for  the  Divine  Fin- 
itude. — ^We  have  been  led  to  conclude  that  God  is  finite  in  both 
senses  of  the  word — ^that  he  is  not  infinite  either  in  the  sense 
of  including  or  possessing  an  infinite  number  of  elements,  or 
in  the  sense  of  including  or  controlling  the  whole  of  reality. 
Our  position  is  therefore  completely  opposed  to  that  of  monis- 
tic idealism,  according  to  which  God  or  the  Absolute  is  infinite 
in  both  these  senses.  It  may  be  well  to  give  a  summary  re- 
statement of  the  reasonings  which  have  led  us  to  this  con- 
clusion. 

{a)  As  Royce  himself  has  shown,  his  conception  of  the 
Absolute  presupposes  the  notion  of  the  realized  infinite.  But 
the  conception  of  a  realized  infinite  is  a  contradiction  in  terms ; 
for  that  which  is  infinite  or  endless  is  not  realized  or  complete. 
And  the  "  new  "  conception  of  infinity  does  not  escape  the  log- 
ical defect  of  the  "  old  " ;  for,  as  we  have  seen,  the  attempt  to 
get  rid  of  the  self-contradiction  by  including  it  in  the  defini- 
tion is  not  satisfactory:  the  contradiction,  though  concealed 
from  view,  still  remains.^ ^"^ 

(6)  The  Absolute  is  said  to  experience  all  in  an  "Eternal 
Now  " ;  but  the  notion  of  an  experience  which  is  itself  "  time- 
less" while  yet  including  experiences  of  temporal  relation  is 
self-contradictory.^^®  Moreover  the  "Eternal  Now"  would  be 
a  realized  infinite,  and  on  that  account,  too,  logically  impos- 
sible.io^ 

(c)  The  Absolute  is  an  all-containing  mind  and  possesses 

lOT  Chapter  VI. 

108  Chapter  II,  Section  2  (6). 

io»  Chapter  VI,  Section  2. 

71 


72  The  Argument  for  a  Finitist  Theology, 

an  all-inclusive  experience.  Now  there  can  be  no  all-inclusive 
experience;  for  it  is  psychologically  impossible  for  certain  of 
the  experiences  of  the  individual  mind,  especially  such  as  are 
conditioned  by  limitation  and  isolation,  to  be  identical  parts 
of  an  all-inclusive  mind.  For  such  a  mind,  by  virtue  of  the 
fact  that  it  is  all-inclusive,  is  unable  to  have  these  experiences. 
And  yet  if  it  does  not  have  them,  it  is  not  all-inclusive.  ^^^ 

(d)  The  identification  of  God  with  the  Absolute  is  vetoed 
by  the  ethical  difficulty  which  besets  every  doctrine  of  the 
divine  omnipotence.  God  is  good;  and,  in  a  world  such  as 
ours,  no  good  being  can  be  omnipotent.  llTot  only  does  this 
objection  hold  against  the  conception  of  the  Absolute,  but 
against  that  of  a  Mind  that  possesses  a  hnowledge  about  all 
things  without  including  everything  as  an  identical  part  of 
its  own  experience;  for,  if  a  Being  were  omniscient  even  in 
this  restricted  sense,  such  a  Being  would  be,  if  not  in  Royce's 
phrase  "world  possessing,''  yet  certainly  world-controlling, 
that  is  to  say,  omnipotent.^^^ 

(e)  The  theory  of  monistic  idealism  is  unsatisfactory  as  a 
practical  philosophy,  inasmuch  as  it  logically  implies  a  life  of 
acquiescence  rather  than  of  action.^  ^^ 

(/)  Considered  as  the  equivalent  of  or  as  a  substitute  for 
the  traditional  idea  of  God,  the  Absolute  is  religiously  inade- 
quate. It  lacks  worth,  and  does  not  satisfy  man's  craving 
for  fellowship  with  a  Person}^^ 

On  the  other  hand,  the  theory  of  a  Supreme  Being  who  is 
limited  in  knowledge  and  power  is  logically  unobjectionable, 
is  not  inconsistent  with  the  presence  of  evil  in  the  world  as  it 
now  is,  implies  the  genuineness  of  human  cooperation  with 
God  in  the  contest  with  evil,  and  offers  man  an  Object  worthy 
of  his  worship,  a  Person  who  desires  his  love. 

3.  The  Difficulties  of  Finitist  Theology. — Let  us  not,  how- 
ever, assume  too  hastily  that  finitist  theology  is  completely 

110  Chapter  H,  Section  2  (6). 

111  Chapters  III  and  IV. 

112  Chapter  II,  Section  2  (c). 
113 Chapter  II,  Section  2  (a). 


Concluding  Reflections  on  Finiiist  Theology,  73 

satisfactory  as  a  religious  doctrine.  Several  questions  present 
themselves : 

(a)  Is  Finitist  Theology  a  Monotheism  or  a  Polytheism? — 
If  God  is  the  whole  of  existence,  or  even  if  he  is  assumed  to 
be  distinct  from,  or  only  a  part  of,  the  universe  but  yet  om- 
nipotent, there  can  be  no  doubt  that  there  is  but  one  God ;  for 
there  can  not  be  more  than  one  whole  of  existence  or  more 
than  one  onmipotent.  If,  however,  we  maintain  that  God  is 
only  a  part  of  being,  and  that  his  power  is  so  limited  that  some 
parts  or  aspects  of  being  are  not  subject  to  his  control,  the 
proposition  that  there  is  but  one  God  is  far  from  self-evident. 

For  most  of  us,  indeed,  the  issue  of  polytheism  versus 
monotheism  does  not  present  a  "  live  option."  It  does  not  ap- 
pear to  have  been  a  live  issue  even  for  William  James. 
Charles  Renouvier,  however,  declines  to  decide  one  way  or 
the  other,  and,  indeed,  is  very  favorably  disposed  toward  poly- 
theism. "  The  doctrine  of  unity,"  he  says,  "  submits  all  the 
beings  of  the  world  to  a  royal  authority  which  varies  from  the 
most  absolute  autocracy  to  a  government  tempered  by  a  meas- 
ure of  liberty  conceded  to  the  subjects."^ ^*  On  the  other  hand, 
the  doctrine  of  a  plurality  of  divine  beings  appears  to  Renou- 
vier  more  accordant  with  republicanism.  "  Polytheism  is  the 
plurality  of  powers  in  the  unity  of  direction."  The  same  con- 
siderations which  make  for  a  belief  in  immortality  lead  Renou- 
vier  to  look  with  favor  upon  the  conception  of  a  plurality  of 
Gods.  He  thinks  it  improbable  that  all  personal  beings  but 
one  should  be  such  as  to  be  included  in  the  class  of  men ;  and, 
like  the  ancients,  supposes  that  men  may  be  raised  to  the  rank 
of  Gods."^ 

One  of  his  interpreters  remarks  that,  though  one  may  at 
first  be  surprised  and  possibly  shocked  by  Renouvier's  evident 
liking  for  polytheism,  the  saint-worship  of  the  Roman  Cath- 
olic Church  would  readily  suggest  such  a  doctrine.  Further- 
more, "the  theology  of  the  Councils  of  Nicsea,  of  Constanti- 

11*  Eenouvier,  Paychologie  rationelle,  Vol.  Ill,  p.  259. 
ii5  76id.,  pp.  255  f. 


74  The  Argument  for  a  Finitist  Theology. 

nople,  of  Chalcedon,  aflSnri,  and  modem  theologians  still  ac- 
cept, the  multiplicity  of  divine  persons.  The  Christian  Trin- 
ity is  not  a  doctrine  of  the  divine  nnity."^^^ 

It  is  true  that  Kenouvier  suggests  that  "  this  polytheism  is 
far  from  being  irreconcilable  with  the  unity  of  God;  .  .  . 
for  the  one  God  would  then  be  the  first  of  the  superhuman 
persons,  rex  hominum  et  deorumJ''^'^'^  It  is,  however,  perfectly 
conceivable  that  there  should  be  a  number  of  superhuman  per- 
sons all  finite  in  power,  and  that  none  of  them  should  be 
"king."  Indeed,  to  anticipate  the  theoretical  doubt  which  is 
discussed  in  the  next  section,  if  all  the  members  of  such  a 
pantheon,  whether  it  were  monarchical  or  democratic  in  its 
organization,  could  be  known  to  be  good,  it  is  not  evident  that 
the  polytheistic  conception  would  be  religiously  unsatisfying. 
However,  as  remarked  above,  the  issue  does  not  present  a  "  live 
option,"  and  it  will  be  better  to  assume,  in  the  further  discus- 
sion, that  there  is  but  one  God. 

(&)  Is  the  Supreme  Being  Good? — ^It  is  true  that  the  log- 
ical motive  for  the  doctrine  that  God  is  finite  is  the  desire  to 
save  his  goodness.  Our  argument  has  been,  God  is  good;  the 
world  is,  in  part,  evil ;  therefore  God's  power  is  limited.  His 
finitude  is  thus  an  inference  from  his  perfect  goodness ;  but  it 
is  evident  that  the  argument  cannot  be  reversed.  The  perfect 
goodness  cannot  be  inferred  from  the  finitude  of  the  Deity. 

If  we  divest  ourselves  of  our  prejudices,  and  forget  the 
affinity  of  the  words  good  and  God,  it  is  possible  to  conceive 
the  existence  of  a  being  who  is  immeasurably  more  powerful 
than  all  others,  and  yet  is  not  good.  Such  a  Supreme  Being 
might  be  defined  as  Power  plus  Intelligence  plus  Conscious 
Purpose.  But  the  purpose  toward  which  the  power  is  directed 
need  not  include  any  concern  for  the  pains  and  pleasures  or 
the  ideal  values  of  humankind.  As  a  man  intent  upon  the  ac- 
complishment of  some  end  goes  his  way,  and  does  not  even 
notice  the  ant-hill  which  his  hurrying  foot  has  demolished,  so 

lie  Arnal,  Philosophie  Beligeuse  de  Charles  Benouvier,  pp.  148  £. 
117  Psychologic  rationcllc,  III,  255. 


Concluding  Reflections  on  Finitist  Theology.  75 

the  Supreme  Purpose  might  seek  its  own  fulfilment  wholly 
regardless  of  the  hopes  and  wishes  of  the  denizens  of  our 
planet.  A  consciously  purposive  Power  wholly  uninterested 
in  the  affairs  of  men  is,  accordingly,  a  logically  possible  con- 
ception of  God. 

Even  the  addition  to  this  conception  of  that  notion  of  an 
interest  in  human  doings  and  sufferings  which,  I  have  said,  is 
not  necessarily  included  in  the  universal  purpose,  does  not 
bring  us  at  once  to  the  Christian  thought  of  a  Father-God.  It 
may  indeed  fall  far  short  of  it.  The  interest  of  the  Supreme 
Power  in  human  affairs  might  be  entirely  non-moral.  It  might 
be  an  interest  in  mundane  happenings  as  a  spectacle.  Such 
a  God  might  take  pleasure  in  the  happiness  of  his  creatures, 
and  also  in  their  pains  and  disappointments,  in  their  sorrows 
as  well  as  in  their  joys.  In  short  God  as  thus  defined  might 
be  a  Supreme  Setebos,  like  him  of  whom  Caliban  muses  in 
Browning's  verse : 

Thinketh  such  shows  nor  right  nor  wrong  in  Him 
Nor  kind,  nor  cruel:  He  is  strong  and  Lord. 
'Am  strong  myself  compared  to  yonder  crabs 
That  march  now  from  the  mountain  to  the  sea; 
'Let  twenty  pass,  and  stone  the  twenty-first, 
Loving  not,  hating  not,  just  choosing  so. 

If,  now,  we  add  to  our  conception  of  a  Supreme  Being  the 
notion  of  moral  quality,  there  still  remains  a  horrible  and 
repulsive  possibility ;  for  moral  quality  may  be  bad  as  well  as 
good.    The  Supreme  Power  might  be  malevolent. 

A  reversal  of  the  traditional  theodicy  is  not  inconceivable. 
Indeed  the  very  argument  by  which  men  have  sought  to  prove 
that  this  is  the  best  might  be  employed  with  a  few  alterations 
to  prove  that  it  is  the  worst  possible  world.  The  elements  of 
goodness  which  mar  the  perfection  of  absolute  evil  might  be 
said  to  be  required  to  set  off  the  evil  by  contrast;  or  the 
Supreme  Fiend  might  be  supposed  to  be  limited  in  his  man- 
agement of  the  universe  by  a  sort  of  "  iron  law  of  wages  " :  a 
certain  amount  of  pleasure  might  be  necessary  to  insure  the 
continuance  of  the  pain-economy. 


76  The  Argument  for  a  Finitist  Theology, 

To  be  sure,  no  one  takes  such  a  possibility  very  seriously; 
yet,  from  the  standpoint  of  mere  logic  and  cold  facts,  it  is  not 
unthinkable.  The  goodness  of  God  cannot  be  proved.  It  can 
only  be  believed;  that  is,  assumed  as  a  working  principle  of 
human  life.  And,  unless  this  assumption  is  made,  the  doc- 
trine of  a  finite  God  has  no  religious  value. 

(c)  Does  the  God  of  Finitist  Theology  Exist? — In  a  dis- 
cussion of  the  adequacy  of  the  idea  of  God  the  existential 
question  can  not  be  wholly  ignored.  It  is  true  that  the  value  of 
the  idea  is  not  wholly  dependent  upon  its  objective  reality  ;^^^ 
yet,  if  a  man  were  convinced  that  the  idea  of  God  is  merely 
an  ideal,  then  for  him  its  value  would  be  seriously  impaired. 
If  the  existence  of  God  is  to  be  proved,  the  demonstration  will 
have  to  consist  in  an  exhibition  of  the  evidences  of  his  pres- 
ence in  the  world.  But  no  one  will  maintain  that  the  argu- 
ment from  design  establishes  more  than  the  prohahility  of 
God's  existence.  Moreover,  if,  without  evidence  of  his 
presence,  we  could  become  convinced  of  his  existence,  mere 
existence  would  not  be  enough.  An  entity  that  does  nothing 
(although  the  thought  of  such  an  entity  might  avail  to  relieve 
one's  loneliness)  would  not  be  completely  adequate.  From  this 
point  of  view  the  question  of  the  existence  of  God  merges  in 
that  of  his  power. 

We  have  criticized  monistic  idealism  on  the  ground  that, 
by  reason  of  its  doctrine  of  the  eternal  perfection  of  the 
Whole,  it  tends  to  quietism,  to  the  mood  of  the  "moral  hol- 
iday." But  there  is  danger  of  reaching  a  similar  position 
from  the  opposite  direction.  The  finite  God  may  be  so  limited 
in  our  thought  of  him  as  to  make  it  doubtful  whether  he  can 
in  any  significant  sense  be  said  to  be  supreme.  Thus  the  same 
modification  that  makes  the  traditional  doctrine  of  God  the- 
oretically tolerable  threatens  to  destroy  its  practical  value. 
For  if  men  should  be  convinced  that,  while  there  is  a  God, 
his  power  and  intelligence  are  not  adequate  to  the  task  of 
world  redemption,  they  would  fall  into  despair;  and  nothing 

118  Mill,  Autobiography;  Vaihinger,  Die  Philosophie  des  als  Ob, 


Concluding  Reflections  on  Finitist  Theology.  77 

so  completely  paralyzes  action  as  despair.  There  is  inspiration 
for  strong  natures  in  the  thought  of  cooperation  with  a  God 
who  actually  needs  our  help ;  but  not  all  are  strong,  and  even 
the  strongest  and  most  daring  spirits  have  their  hours  of  de- 
pression, when  they  need  to  feel  that  there  is  sufficient  power 
on  their  side  to  assure  the  ultimate  victory  of  the  Eight.  From 
this  point  of  view  the  question  of  God's  existence  is  equivalent 
to  a  question  about  the  salvability  of  the  world.  It  may,  ac- 
cordingly, be  rephrased  thus:  Is  there,  in  this  world  of  ours, 
sufficient  power  and  intelligence  in  the  service  of  good  will,  to 
assure  the  realization  and  preservation  of  the  values  that  wd 
hold  dear? 

4.  Finitist  Theology  and  the  Bight  to  Believe, — By  Wil- 
liam James  finitist  theology  is  combined  with  a  doctrine  of 
the  "  will  to  believe."  The  existence  of  God  can  not  be  proved 
by  scientific  methods  of  demonstration.  Considered  jas  a 
hypothesis  it  is,  indeed,  not  inconsistent  with  the  facts;  but 
neither  is  the  contrary  hypothesis.  'Now,  says  James,  this  is 
a  case  where  we  ought  to  practise  the  will  to  believe.  "  Our 
passional  nature  not  only  lawfully  may,  but  must,  decide  an 
option  between  propositions,  whenever  it  is  a  genuine  option 
that  cannot  by  its  nature  be  decided  on  intellectual  grounds."^^® 
In  other  words,  though  James  nowhere  puts  it  in  just  this 
way,  we  are  at  liberty  to  act  as  if  we  were  certain  of  God' 9' 
existence,  even  if  we  have  no  intellectual  grounds,  or  have  only 
insufficient  grounds,  for  certainty. 

There  are,  however,  obvious  objections  to  this  procedure. 
It  seems  to  encourage  the  all  too  common  tendency  to  super- 
ficial thinking,  where  one's  own  interests  and  prejudices  are 
involved ;  and  there  appears  to  be  a  suggestion  of  intellectual 
dishonesty  in  the  proposal  to  believe  when  there  is  not  sufficient 
evidence  to  convince  the  reason.  In  my  opinion,  however, 
these  objections  are  based  upon  a  failure  to  distinguish  be- 
tween different  senses  of  the  word  "  believe."    It  must  be  ad- 

ii»  The  Will  to  Believe,  p.  27. 


78  The  Argument  for  a  Finitist  Theology. 

mitted,  I  fear,  that  James  himself  is  partly  responsible  for 
these  confusions. 

There  are  at  least  three  kinds  of  "believing.''  In  the  first 
place,  one  may  be  said  to  believe  when  he  feels  that  he  knows. 
Secondly,  belief  may  be  understood  in  a  wholly  practical 
sense.  One  shows  his  faith  by  his  works;  and  it  is  easy  to 
pass  from  this  principle  to  the  view  that  faith,  or  belief,  is 
the  action  which  would  normally  accompany  or  result  from 
belief  in  the  first  sense.  It  is  this  second  sense  of  believing, 
the  acting  as  if  one  knew,  which  James  seems  to  have  chiefly 
in  mind  when  he  speaks  of  a  "  will  to  believe." 

There  is,  however,  a  third  sense  of  the  word  "believe," 
which  seems  to  be  implied,  though  not  clearly  distinguished 
from  the  others,  in  James's  exposition.  It  differs  from  our 
first  sense  in  being  without  real  or  supposed  theoretical  jus- 
tification; and  from  the  second  in  being  an  affair  of  feeling, 
rather  than  of  will  or  action.  If  the  first  kind  of  believing 
is  the  '^ feeling  that  one  knows,"  and  the  second,  "the  acting 
as  if  one  hnew/'  the  third  may  be  said  to  be  "the  feeling  05 
if  one  knew/' 

That  this  third  kind  of  belief  is  psychologically  possible 
is  a  matter  of  everyday  experience.  Our  feelings  are  seldom 
quite  appropriate  to  the  theoretical  situation.  The  passenger 
on  the  railway  train  who  is  nervous  and  ill  at  ease  because  of 
the  fear  of  a  wreck  is  permitting  emotion  to  outrun  the  evi- 
dence. But  the  same  is  true  of  the  passenger  who  has  no 
feeling  of  anxiety  whatever;  for  there  is  some  danger.  And, 
while  the  probability  of  a  wreck  is  not  sufficiently  great  to 
justify  the  fears  of  the  one,  it  is  not  so  small  as  to  justify  the 
utter  calm  of  the  other.  Belief,  in  the  third  sense,  the  feeling 
as  one  would  feel  if  one  had  theoretical  knowledge  which  he 
does  not  have,  is  thus  illustrated  by  our  usual  freedom  from 
emotional  disturbance  on  a  rapidly  moving  train.  We  know 
that  a  thousand  and  one  things  might  happen,  any  one  of 
which  might  plunge  us  to  almost  instant  death;  we  may  be 
theoretically   persuaded  that   there   are   a  given   number  of 


Concluding  Reflections  on  Finitist  Theology.  79 

chances  in  ten  million  that  we  will  on  this  particular  day  be 
killed  in  a  wreck ;  we  may  even  allow  our  minds  to  dwell  upon 
these  chances  of  destruction ;  and  yet  feel  as  we  should  feel  if 
the  chance  were  absolutely  nil. 

This  sort  of  belief  is  even  better  illustrated  in  our  social 
relations.  Here,  too,  the  degree  of  certainty  which  we  feel  is 
not  usually  the  exact  degree  that  would  be  logically  appro- 
priate to  the  situation.  We  cannot,  prove  that  the  bank  will 
not  fail;  that  people  are  telling  us  the  truth;  that  our  best 
friends  will  not  play  us  false ;  that  the  Causes  to  which  we  de- 
vote ourselves  are  really  worthy  of  our  devotion.  We  can  have 
no  intellectual  certainty  in  regard  to  these  matters;  and  yet 
we  not  only  act  but  also  feel  as  we  should  act  and  feel  if  we 
were  intellectually  certain.  In  a  word,  our  faiths  and  loyal- 
ties habitually  outrun  the  evidence. 

In  the  same  way,  although  we  do  not  hnow  that  there  is  a 
God,  or  that  the  world  is  moving  toward  a  worthy  goal,  and 
cannot  therefore  be  said  to  believe  in  the  existence  of  God  or 
in  the  salvability  of  the  world  in  the  first  of  our  three  senses 
of  the  word  "  believe,"  we  have  the  right  to  believe  in  the  other 
two  senses.  We  are  justified  in  accepting  the  existence  of 
God  as  an  assumption  in  accordance  with  which  to  plan  our 
lives;  and  also  in  feeling  a  greater  degree  of  certainty  with 
reference  to  his  existence  than  is  theoretically  warranted. 


BIBLIOGKAPHY. 

Aenal,  Andre.  La  Philosophie  Religieuse  de  Charles  Renouvier. 
Paris,  1907. 

B'OWNE,  B.  p.  Metaphysics:  A  Study  in  First  Principles.  New 
York,  1882. 

Bradley,  F.  H.  Appearance  and  Reality:  A  Metaphysical  Essay. 
London,  1902. 

Cantor,  Georg.  Beitrage  zur  Begriindung  der  transfiniten  Mengen- 
lehre.  Translated  by  Philip  E.  B.  Jourdain  as  "  Contributions 
to  the  Founding  of  the  Theory  of  Transfinite  Numbers."  Chi- 
cago, 1915. 

Clarke,  W.  N.    The  Christian  Doctrine  of  God.    New  York,  1909. 

CounjRAT,  Louis.    De  L'Infini  Mathematique.    Paris,  1896. 

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VITA. 

Eay  Harbaugh  Dotterer  was  born  in  Westmoreland  County, 
Pennsylvania,  Aug.  4,  1880.  He  attended  the  public  schools, 
and  taught  two  terms.  In  1902,  he  was  graduated  at  the  Cen- 
tral State  !N'ormal  School,  Lock  Haven,  Pa.;  in  1906,  at 
Franklin  and  Marshall  College;  in  1909,  at  the  Theological 
Seminary  of  the  Eeformed  Church,  Lancaster,  Pa.  From 
June,  1909,  to  January,  1913,  he  was  pastor  of  a  Reformed 
Church  at  Eockwood,  Pa.,  and  from  1913  to  the  present,  in 
Baltimore,  Md.  In  1910,  he  completed  a  graduate  course,  and 
received  the  degree  of  Ph.M.  from  Franklin  and  Marshall  Col- 
lege. Since  October,  1913,  he  has  been  a  student  in  the  Johns 
Hopkins  University.  His  subjects  have  been  Philosophy, 
Psychology,  and  Education.  In  1916  he  received  the  degree 
of  Master  of  Arts,  having  submitted  an  essay  on  "  The  Philos- 
ophy of  the  '  As  If '  in  its  Application  to  Theology.'' 


88 


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